Math Trig/Calc help?

Question

Given a right triangle ABC with a=13 and b=26, find the value of angle A, angle B, and side length c. Round to the nearest thousandth.

Answer 1

Given

a=13

b=26

For any right triangled,One angle is equals to 90º.

In given problem we need to find angles A,B (unknown angles).

So C should be known.So consider C = 90º.

For a right triangle ABC

c² = a² + b²

c² = 12² + 26²

c² = 820

c = 28.64

sinB = b/c

sinB = 26/28.64

B = sin^-1(0.9078)

B = 65.2º

Total of all angles in a triangle is 180º

A + B + C =180

A = 180 - B - C

A = 180 - 65.2 - 90

A = 24.8º

Solution :

Side length c =28.64

Angles B = 65.2º and A = 24.8º