Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse. tan(A) = 5/12 , b = 2

Question

I have to find a=?

I have to find c=?

Answer 1

Right triangle ABC,,,,

C is the right angle,

B on the bottom, C directly above B and A on the right

b = AC = 2

A = inverse_tangent(5/12) = 22.619....

cos A = b/c = 2/c

c = 2/ cos A = 2 / cos 22.619... = 13/6

sin A = a/c = 6a/13

a = 13* sin A / 6 = 13 * sin 22.619.../6 = 5/6

Note that tan A = 5/6 divided by 2 = 5/12 as given