Triangle ABC is a right triangle and cos (22.6o) = B/13. Solve for b and round to the nearest whole number.

Which equation correctly uses the value of b to solve for a?

tan (22.6o) = a/13

tan (22.6o) = 13/a

tan (22.6o) = a/12

tan (22.6o) = 12/a

The cosine of an angle is equal to the adjacent side divided by the hypotenuse. In a right triangle, the hypotenuse is the longest side. Its value is 13. It also follows that B is the adjacent side.

To solve for B,

B = 13 cos 22.6˚ = 12

The tangent of the angle is equal to the opposite side divided by the adjacent side. Since B is known, therefore the answer is

tan (22.6˚) = a/12