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

Given $\cos(22.6^{\circ})=\frac{b}{13}$, we can solve for b by multiplying both sides by 13. So $b = 13\times\cos(22.6^{\circ})$. Using a calculator, $\cos(22.6^{\circ})\approx0.923$, then $b = 13\times0.923 = 11.999\approx12$.

Step2: Determine the correct tangent - based equation for a

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle A = 22.6^{\circ}$, $\tan(22.6^{\circ})=\frac{a}{b}$. Since $b\approx12$, the correct equation is $\tan(22.6^{\circ})=\frac{a}{12}$.

Answer:

$\tan(22.6^{\circ})=\frac{a}{12}$