Question

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

Answer 1

Answer: It's C, tan(22.6°) = a/12

Step-by-step explanation: You first have to solve for b, which the equation is already set up. Once done solving, your answer is 12. b and a are what's going to be used to solve the problem, and because they are our opposite and adjacent, we use tangent. a is our opposite so it's going to be at the top AKA our numerator. b, which is 12, is our adjacent. It's going to be on the bottom AKA our denominator. Therefore, with all this information we can conclude that the answer is C.

Answer 2

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