Question

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

Explanation:

Step1: Recall cosine definition in right - triangle

In right - triangle \(ABC\) with \(\angle A = 22.6^{\circ}\), \(\cos(A)=\frac{adjacent}{hypotenuse}\). Given \(\cos(22.6^{\circ})=\frac{13}{b}\), we can solve for \(b\).
\[b=\frac{13}{\cos(22.6^{\circ})}\]
Since \(\cos(22.6^{\circ})\approx0.923\), then \(b=\frac{13}{0.923}\approx14\) cm.

Step2: Recall tangent definition in right - triangle

The tangent of an angle in a right - triangle is defined as \(\tan(A)=\frac{opposite}{adjacent}\). For \(\angle A = 22.6^{\circ}\), \(\tan(22.6^{\circ})=\frac{a}{13}\).

Answer:

The equation that correctly uses the value of \(b\) to solve for \(a\) is \(\tan(22.6^{\circ})=\frac{a}{13}\).