Triangle - What is the length of the hypotenuse?

$\begingroup$

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.

$\endgroup$ 2

2 Answers

$\begingroup$

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 $AB=AD+BD=7+\frac {25}7=\frac {74}7$

$\endgroup$ $\begingroup$

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.

$\endgroup$ 2

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy