Question

triangle abc is a right - triangle and cos(22.6°) = 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(22.6°) = a/13; tan(22.6°) = 13/a; tan(22.6°) = a/12; tan(22.6°) = 12/a

Explanation:

Step1: Solve for b using cosine

$b = 13 \times \cos(22.6^\circ) \approx 13 \times 0.923 \approx 12$

Step2: Identify tan relation for a

$\tan(22.6^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{a}{b} = \frac{a}{12}$

Answer:

12, C. tan(22.6°) = a/12