Question

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

Explanation:

Step1: Recall tangent formula

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

Step2: Apply the formula

We have $\tan(30^{\circ})=\frac{b}{8}$.

Step3: Solve for $b$

Cross - multiply to get $b = 8\tan(30^{\circ})$.

Answer:

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