Triangle - What is the length of the hypotenuse?

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$begingroup$


Triangle ABC has a right angle at corner C. It has a height from C to a point D on side |AB|. If |CD|=5 and |AD|=7 then what is the length of the hypotenuse? (|AB|=?)



Correct Answer: 74/7



I have tried solving the question above by the help of the law of cosines and sines, pythagoras theorm and uniform triangles but without much success. I always tend to get to many unknown variables. Thanks in advance.






geometry triangle







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  • $begingroup$
    right $triangle$-s ACD and ACB are similar, since they share angle a. Therefore, $|AD|/|CD| = |AC|/|BC|.
    $endgroup$
    – user2661923
    May 2 '18 at 23:17












  • $begingroup$
    @IGotAQuestion Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here meta.stackexchange.com/questions/5234/…
    $endgroup$
    – gimusi
    May 31 '18 at 19:49
















0












$begingroup$


Triangle ABC has a right angle at corner C. It has a height from C to a point D on side |AB|. If |CD|=5 and |AD|=7 then what is the length of the hypotenuse? (|AB|=?)



Correct Answer: 74/7



I have tried solving the question above by the help of the law of cosines and sines, pythagoras theorm and uniform triangles but without much success. I always tend to get to many unknown variables. Thanks in advance.






geometry triangle







share|cite|improve this question









$endgroup$












  • $begingroup$
    right $triangle$-s ACD and ACB are similar, since they share angle a. Therefore, $|AD|/|CD| = |AC|/|BC|.
    $endgroup$
    – user2661923
    May 2 '18 at 23:17












  • $begingroup$
    @IGotAQuestion Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here meta.stackexchange.com/questions/5234/…
    $endgroup$
    – gimusi
    May 31 '18 at 19:49














0












0








0





$begingroup$


Triangle ABC has a right angle at corner C. It has a height from C to a point D on side |AB|. If |CD|=5 and |AD|=7 then what is the length of the hypotenuse? (|AB|=?)



Correct Answer: 74/7



I have tried solving the question above by the help of the law of cosines and sines, pythagoras theorm and uniform triangles but without much success. I always tend to get to many unknown variables. Thanks in advance.






geometry triangle







share|cite|improve this question









$endgroup$




Triangle ABC has a right angle at corner C. It has a height from C to a point D on side |AB|. If |CD|=5 and |AD|=7 then what is the length of the hypotenuse? (|AB|=?)



Correct Answer: 74/7



I have tried solving the question above by the help of the law of cosines and sines, pythagoras theorm and uniform triangles but without much success. I always tend to get to many unknown variables. Thanks in advance.






geometry triangle




geometry triangle






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked May 2 '18 at 23:06









IGotAQuestionIGotAQuestion

186




186












  • $begingroup$
    right $triangle$-s ACD and ACB are similar, since they share angle a. Therefore, $|AD|/|CD| = |AC|/|BC|.
    $endgroup$
    – user2661923
    May 2 '18 at 23:17












  • $begingroup$
    @IGotAQuestion Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here meta.stackexchange.com/questions/5234/…
    $endgroup$
    – gimusi
    May 31 '18 at 19:49


















  • $begingroup$
    right $triangle$-s ACD and ACB are similar, since they share angle a. Therefore, $|AD|/|CD| = |AC|/|BC|.
    $endgroup$
    – user2661923
    May 2 '18 at 23:17












  • $begingroup$
    @IGotAQuestion Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here meta.stackexchange.com/questions/5234/…
    $endgroup$
    – gimusi
    May 31 '18 at 19:49
















$begingroup$
right $triangle$-s ACD and ACB are similar, since they share angle a. Therefore, $|AD|/|CD| = |AC|/|BC|.
$endgroup$
– user2661923
May 2 '18 at 23:17






$begingroup$
right $triangle$-s ACD and ACB are similar, since they share angle a. Therefore, $|AD|/|CD| = |AC|/|BC|.
$endgroup$
– user2661923
May 2 '18 at 23:17














$begingroup$
@IGotAQuestion Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here meta.stackexchange.com/questions/5234/…
$endgroup$
– gimusi
May 31 '18 at 19:49




$begingroup$
@IGotAQuestion Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here meta.stackexchange.com/questions/5234/…
$endgroup$
– gimusi
May 31 '18 at 19:49










3 Answers
3






active

oldest

votes


















-1












$begingroup$

Draw a picture. You just need similar triangles. $ABC,ACD,$ and $CBD$ are similar. $frac {BD}{DC}=frac {CD}{AD}=frac 57$ so $BD=frac {25}7$ and $AB=AD+BD=7+frac {25}7=frac {74}7$






share|cite|improve this answer









$endgroup$





















    -1












    $begingroup$

    Remember that the height, $CD$, will be perpendicular to side $AB$. You can use Pythagorean Theorem to find length $AC$. Hint: Can you find the angle $angle CBA$? This will help you.






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
      $endgroup$
      – IGotAQuestion
      May 2 '18 at 23:20










    • $begingroup$
      The height (or altitude) of a triangle referenced to side $b$ must be perpendicular to $b$. You could also look at the other answers. There are probably many ways of solving it.
      $endgroup$
      – D.B.
      May 2 '18 at 23:23



















    -1












    $begingroup$

    HINT




    • make a sketch of the triangle

    • by Pytagoras find $AC$ from $AC^2=CD^2+AD^2$

    • then use similarity to find that $frac{AB}{AC}=frac{AC}{AD}$


    enter image description here






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
      $endgroup$
      – IGotAQuestion
      May 2 '18 at 23:22










    • $begingroup$
      it is true by definition of height, the height from a vertex is always perpendicular to the opposite side en.wikipedia.org/wiki/Altitude_(triangle)
      $endgroup$
      – gimusi
      May 2 '18 at 23:23












    • $begingroup$
      So if it says that a height is drawn from an angle, it is always perpendicular to the side it is drawn? Thanks!
      $endgroup$
      – IGotAQuestion
      May 2 '18 at 23:24










    • $begingroup$
      @IGotAQuestion Yes exactly, take a look to the link for the definition.
      $endgroup$
      – gimusi
      May 2 '18 at 23:25











    Your Answer





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    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    -1












    $begingroup$

    Draw a picture. You just need similar triangles. $ABC,ACD,$ and $CBD$ are similar. $frac {BD}{DC}=frac {CD}{AD}=frac 57$ so $BD=frac {25}7$ and $AB=AD+BD=7+frac {25}7=frac {74}7$






    share|cite|improve this answer









    $endgroup$


















      -1












      $begingroup$

      Draw a picture. You just need similar triangles. $ABC,ACD,$ and $CBD$ are similar. $frac {BD}{DC}=frac {CD}{AD}=frac 57$ so $BD=frac {25}7$ and $AB=AD+BD=7+frac {25}7=frac {74}7$






      share|cite|improve this answer









      $endgroup$
















        -1












        -1








        -1





        $begingroup$

        Draw a picture. You just need similar triangles. $ABC,ACD,$ and $CBD$ are similar. $frac {BD}{DC}=frac {CD}{AD}=frac 57$ so $BD=frac {25}7$ and $AB=AD+BD=7+frac {25}7=frac {74}7$






        share|cite|improve this answer









        $endgroup$



        Draw a picture. You just need similar triangles. $ABC,ACD,$ and $CBD$ are similar. $frac {BD}{DC}=frac {CD}{AD}=frac 57$ so $BD=frac {25}7$ and $AB=AD+BD=7+frac {25}7=frac {74}7$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered May 2 '18 at 23:15









        Ross MillikanRoss Millikan

        295k23198371




        295k23198371























            -1












            $begingroup$

            Remember that the height, $CD$, will be perpendicular to side $AB$. You can use Pythagorean Theorem to find length $AC$. Hint: Can you find the angle $angle CBA$? This will help you.






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:20










            • $begingroup$
              The height (or altitude) of a triangle referenced to side $b$ must be perpendicular to $b$. You could also look at the other answers. There are probably many ways of solving it.
              $endgroup$
              – D.B.
              May 2 '18 at 23:23
















            -1












            $begingroup$

            Remember that the height, $CD$, will be perpendicular to side $AB$. You can use Pythagorean Theorem to find length $AC$. Hint: Can you find the angle $angle CBA$? This will help you.






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:20










            • $begingroup$
              The height (or altitude) of a triangle referenced to side $b$ must be perpendicular to $b$. You could also look at the other answers. There are probably many ways of solving it.
              $endgroup$
              – D.B.
              May 2 '18 at 23:23














            -1












            -1








            -1





            $begingroup$

            Remember that the height, $CD$, will be perpendicular to side $AB$. You can use Pythagorean Theorem to find length $AC$. Hint: Can you find the angle $angle CBA$? This will help you.






            share|cite|improve this answer









            $endgroup$



            Remember that the height, $CD$, will be perpendicular to side $AB$. You can use Pythagorean Theorem to find length $AC$. Hint: Can you find the angle $angle CBA$? This will help you.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered May 2 '18 at 23:16









            D.B.D.B.

            1,2708




            1,2708












            • $begingroup$
              How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:20










            • $begingroup$
              The height (or altitude) of a triangle referenced to side $b$ must be perpendicular to $b$. You could also look at the other answers. There are probably many ways of solving it.
              $endgroup$
              – D.B.
              May 2 '18 at 23:23


















            • $begingroup$
              How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:20










            • $begingroup$
              The height (or altitude) of a triangle referenced to side $b$ must be perpendicular to $b$. You could also look at the other answers. There are probably many ways of solving it.
              $endgroup$
              – D.B.
              May 2 '18 at 23:23
















            $begingroup$
            How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
            $endgroup$
            – IGotAQuestion
            May 2 '18 at 23:20




            $begingroup$
            How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
            $endgroup$
            – IGotAQuestion
            May 2 '18 at 23:20












            $begingroup$
            The height (or altitude) of a triangle referenced to side $b$ must be perpendicular to $b$. You could also look at the other answers. There are probably many ways of solving it.
            $endgroup$
            – D.B.
            May 2 '18 at 23:23




            $begingroup$
            The height (or altitude) of a triangle referenced to side $b$ must be perpendicular to $b$. You could also look at the other answers. There are probably many ways of solving it.
            $endgroup$
            – D.B.
            May 2 '18 at 23:23











            -1












            $begingroup$

            HINT




            • make a sketch of the triangle

            • by Pytagoras find $AC$ from $AC^2=CD^2+AD^2$

            • then use similarity to find that $frac{AB}{AC}=frac{AC}{AD}$


            enter image description here






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:22










            • $begingroup$
              it is true by definition of height, the height from a vertex is always perpendicular to the opposite side en.wikipedia.org/wiki/Altitude_(triangle)
              $endgroup$
              – gimusi
              May 2 '18 at 23:23












            • $begingroup$
              So if it says that a height is drawn from an angle, it is always perpendicular to the side it is drawn? Thanks!
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:24










            • $begingroup$
              @IGotAQuestion Yes exactly, take a look to the link for the definition.
              $endgroup$
              – gimusi
              May 2 '18 at 23:25
















            -1












            $begingroup$

            HINT




            • make a sketch of the triangle

            • by Pytagoras find $AC$ from $AC^2=CD^2+AD^2$

            • then use similarity to find that $frac{AB}{AC}=frac{AC}{AD}$


            enter image description here






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:22










            • $begingroup$
              it is true by definition of height, the height from a vertex is always perpendicular to the opposite side en.wikipedia.org/wiki/Altitude_(triangle)
              $endgroup$
              – gimusi
              May 2 '18 at 23:23












            • $begingroup$
              So if it says that a height is drawn from an angle, it is always perpendicular to the side it is drawn? Thanks!
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:24










            • $begingroup$
              @IGotAQuestion Yes exactly, take a look to the link for the definition.
              $endgroup$
              – gimusi
              May 2 '18 at 23:25














            -1












            -1








            -1





            $begingroup$

            HINT




            • make a sketch of the triangle

            • by Pytagoras find $AC$ from $AC^2=CD^2+AD^2$

            • then use similarity to find that $frac{AB}{AC}=frac{AC}{AD}$


            enter image description here






            share|cite|improve this answer









            $endgroup$



            HINT




            • make a sketch of the triangle

            • by Pytagoras find $AC$ from $AC^2=CD^2+AD^2$

            • then use similarity to find that $frac{AB}{AC}=frac{AC}{AD}$


            enter image description here







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered May 2 '18 at 23:19









            gimusigimusi

            92.8k84494




            92.8k84494












            • $begingroup$
              How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:22










            • $begingroup$
              it is true by definition of height, the height from a vertex is always perpendicular to the opposite side en.wikipedia.org/wiki/Altitude_(triangle)
              $endgroup$
              – gimusi
              May 2 '18 at 23:23












            • $begingroup$
              So if it says that a height is drawn from an angle, it is always perpendicular to the side it is drawn? Thanks!
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:24










            • $begingroup$
              @IGotAQuestion Yes exactly, take a look to the link for the definition.
              $endgroup$
              – gimusi
              May 2 '18 at 23:25


















            • $begingroup$
              How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:22










            • $begingroup$
              it is true by definition of height, the height from a vertex is always perpendicular to the opposite side en.wikipedia.org/wiki/Altitude_(triangle)
              $endgroup$
              – gimusi
              May 2 '18 at 23:23












            • $begingroup$
              So if it says that a height is drawn from an angle, it is always perpendicular to the side it is drawn? Thanks!
              $endgroup$
              – IGotAQuestion
              May 2 '18 at 23:24










            • $begingroup$
              @IGotAQuestion Yes exactly, take a look to the link for the definition.
              $endgroup$
              – gimusi
              May 2 '18 at 23:25
















            $begingroup$
            How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
            $endgroup$
            – IGotAQuestion
            May 2 '18 at 23:22




            $begingroup$
            How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption.
            $endgroup$
            – IGotAQuestion
            May 2 '18 at 23:22












            $begingroup$
            it is true by definition of height, the height from a vertex is always perpendicular to the opposite side en.wikipedia.org/wiki/Altitude_(triangle)
            $endgroup$
            – gimusi
            May 2 '18 at 23:23






            $begingroup$
            it is true by definition of height, the height from a vertex is always perpendicular to the opposite side en.wikipedia.org/wiki/Altitude_(triangle)
            $endgroup$
            – gimusi
            May 2 '18 at 23:23














            $begingroup$
            So if it says that a height is drawn from an angle, it is always perpendicular to the side it is drawn? Thanks!
            $endgroup$
            – IGotAQuestion
            May 2 '18 at 23:24




            $begingroup$
            So if it says that a height is drawn from an angle, it is always perpendicular to the side it is drawn? Thanks!
            $endgroup$
            – IGotAQuestion
            May 2 '18 at 23:24












            $begingroup$
            @IGotAQuestion Yes exactly, take a look to the link for the definition.
            $endgroup$
            – gimusi
            May 2 '18 at 23:25




            $begingroup$
            @IGotAQuestion Yes exactly, take a look to the link for the definition.
            $endgroup$
            – gimusi
            May 2 '18 at 23:25


















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