Triangle - What is the length of the hypotenuse?

Question

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.

Answer 1

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

Answer 2

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.