# Triangle - What is the length of the hypotenuse?

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|=?)

• right $\triangle$-s ACD and ACB are similar, since they share angle a. Therefore, $|AD|/|CD| = |AC|/|BC|. – user2661923 May 2 '18 at 23:17 • @IGotAQuestion Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here meta.stackexchange.com/questions/5234/… – user May 31 '18 at 19:49 ## 3 Answers Draw a picture. You just need similar triangles.$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$Remember that the height,$CD$, will be perpendicular to side$AB$. You can use Pythagorean Theorem to find length$AC$. Hint: Can you find the angle$\angle CBA$? This will help you. • How can you know that the height CD will be perpendicular to AB? It seems to me to be an anjustified assumption. – IGotAQuestion May 2 '18 at 23:20 • The height (or altitude) of a triangle referenced to side$b$must be perpendicular to$b$. You could also look at the other answers. There are probably many ways of solving it. – D.B. May 2 '18 at 23:23 HINT • make a sketch of the triangle • by Pytagoras find$AC$from$AC^2=CD^2+AD^2$• then use similarity to find that$\frac{AB}{AC}=\frac{AC}{AD}\$ 