Triangle - What is the length of the hypotenuse?
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
asked May 2 '18 at 23:06
IGotAQuestionIGotAQuestion
186
$endgroup$
add a comment |
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
asked May 2 '18 at 23:06
IGotAQuestionIGotAQuestion
186
$endgroup$
$begingroup$
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
add a comment |
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
asked May 2 '18 at 23:06
IGotAQuestionIGotAQuestion
186
$endgroup$
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
asked May 2 '18 at 23:06
IGotAQuestionIGotAQuestion
186
asked May 2 '18 at 23:06
IGotAQuestionIGotAQuestion
186
asked May 2 '18 at 23:06
IGotAQuestionIGotAQuestion
186
asked May 2 '18 at 23:06
IGotAQuestionIGotAQuestion
186
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
add a comment |
$begingroup$
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
add a comment |
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 $AB=AD+BD=7+frac {25}7=frac {74}7$
answered May 2 '18 at 23:15
Ross MillikanRoss Millikan
295k23198371
$endgroup$
add a comment |
-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.
answered May 2 '18 at 23:16
D.B.D.B.
1,2708
$endgroup$
$begingroup$
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
add a comment |
-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 $frac{AB}{AC}=frac{AC}{AD}$
answered May 2 '18 at 23:19
gimusigimusi
92.8k84494
$endgroup$
$begingroup$
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
add a comment |
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 $AB=AD+BD=7+frac {25}7=frac {74}7$
answered May 2 '18 at 23:15
Ross MillikanRoss Millikan
295k23198371
$endgroup$
add a comment |
-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 $AB=AD+BD=7+frac {25}7=frac {74}7$
answered May 2 '18 at 23:15
Ross MillikanRoss Millikan
295k23198371
$endgroup$
add a comment |
-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 $AB=AD+BD=7+frac {25}7=frac {74}7$
answered May 2 '18 at 23:15
Ross MillikanRoss Millikan
295k23198371
$endgroup$
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 $AB=AD+BD=7+frac {25}7=frac {74}7$
answered May 2 '18 at 23:15
Ross MillikanRoss Millikan
295k23198371
answered May 2 '18 at 23:15
Ross MillikanRoss Millikan
295k23198371
answered May 2 '18 at 23:15
Ross MillikanRoss Millikan
295k23198371
answered May 2 '18 at 23:15
Ross MillikanRoss Millikan
295k23198371
295k23198371
add a comment |
add a comment |
-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.
answered May 2 '18 at 23:16
D.B.D.B.
1,2708
$endgroup$
$begingroup$
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
add a comment |
-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.
answered May 2 '18 at 23:16
D.B.D.B.
1,2708
$endgroup$
$begingroup$
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
add a comment |
-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.
answered May 2 '18 at 23:16
D.B.D.B.
1,2708
$endgroup$
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.
answered May 2 '18 at 23:16
D.B.D.B.
1,2708
answered May 2 '18 at 23:16
D.B.D.B.
1,2708
answered May 2 '18 at 23:16
D.B.D.B.
1,2708
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
add a comment |
$begingroup$
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
add a comment |
-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 $frac{AB}{AC}=frac{AC}{AD}$
answered May 2 '18 at 23:19
gimusigimusi
92.8k84494
$endgroup$
$begingroup$
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
add a comment |
-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 $frac{AB}{AC}=frac{AC}{AD}$
answered May 2 '18 at 23:19
gimusigimusi
92.8k84494
$endgroup$
$begingroup$
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
add a comment |
-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 $frac{AB}{AC}=frac{AC}{AD}$
answered May 2 '18 at 23:19
gimusigimusi
92.8k84494
$endgroup$
HINT
- make a sketch of the triangle
- by Pytagoras find $AC$ from $AC^2=CD^2+AD^2$
- then use similarity to find that $frac{AB}{AC}=frac{AC}{AD}$
answered May 2 '18 at 23:19
gimusigimusi
92.8k84494
answered May 2 '18 at 23:19
gimusigimusi
92.8k84494
answered May 2 '18 at 23:19
gimusigimusi
92.8k84494
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
add a comment |
$begingroup$
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
add a comment |
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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