find sides of a triangle with only cos and one side

Question

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.

cos B = 3/5 , a = 27

Find b =

Find c =

I'm really struggling with this problem and others like it. I'm not sure where to begin. The fact the it's the cosine of angle B is throwing me off. Any push in the right direction is appreciated.

Answer 1

Thanks Billy,

Considering that cosB = 3/5, we will need to multiply both sides by cos-1 (inverse of cosine) to find angle B

When doing so, we will now have (cos-1)(cosB) = (cos-1 *(3/5)), giving us angle B = 53 degrees (approx.)

Now we know Angle B = 53 degrees, meaning that Angle C (the hypotenuse angle) will equal 90 degrees

Knowing that the right triangle will equal 180 degrees total, this means that the remainder angle A will equal:

Angle A = 180 - (90 + 53) = 37 degrees

In order to find the values of the sides of the triangle, we will need a graphic/ image in order to know the relative positions of each.

Hopefully this helps!