Question

Use the given information to find the lengths of the other two sides of the right triangle if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.
tan(A) = 7/9, b = 4

I already found (a) which is 28/9, I just need to find c =

Answer 1

c = $\frac{4\sqrt{30} }{9}$

using Pythagoras' identity on the right triangle

c = √( 4² + ($\frac{28}{9}$ )² ) = √16 + $\frac{2080}{81}$

 = $\frac{\sqrt{2080} }{9}$ = $\frac{4\sqrt{130} }{9}$