Question

triangle abc is given. if cos(a) = 12/13, what is sin(b)? a. 12/13 b. 5/12 c. 13/12 d. 5/13

Explanation:

Step1: Recall angle - relationship in right - triangle

In right - triangle \(ABC\) with right - angle at \(C\), \(\angle A+\angle B = 90^{\circ}\). So, \(\sin(B)=\cos(A)\).

Step2: Use the given value of \(\cos(A)\)

Given that \(\cos(A)=\frac{12}{13}\), then \(\sin(B)=\frac{12}{13}\) since \(\sin(B)=\cos(A)\) for complementary angles \(A\) and \(B\) in a right - triangle.

Answer:

A. \(\frac{12}{13}\)