Question

which equation can be used to solve for b? b = (8)sin(30°) b = (8)tan(30°) b = sin(30°)/8 b = tan(30°)/8

Explanation:

Step1: Recall tangent - ratio in right - triangle

In right - triangle \(ABC\) with right - angle at \(C\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 30^{\circ}\), the side opposite to \(\angle B\) is \(b\) and the side adjacent to \(\angle B\) is \(8\) ft.
So, \(\tan(30^{\circ})=\frac{b}{8}\).

Step2: Solve for \(b\)

Multiply both sides of the equation \(\tan(30^{\circ})=\frac{b}{8}\) by \(8\). We get \(b = 8\tan(30^{\circ})\).

Answer:

\(b=(8)\tan(30^{\circ})\)