Question

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

Explanation:

Step1: Recall tangent - ratio in right - triangle

In a right - triangle, the tangent of an acute angle is the ratio of the opposite side to the adjacent side. For angle \(B = 30^{\circ}\) in right - triangle \(ABC\) with right - angle at \(C\), \(\tan B=\frac{\text{opposite}}{\text{adjacent}}\). Here, 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 \(b\)

Cross - multiply the equation \(\tan(30^{\circ})=\frac{b}{8}\) to get \(b = 8\times\tan(30^{\circ})\).

Answer:

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