Question

which equation can be used to solve for b? tan(30°)=10/b tan(30°)=b/10 tan(30°)=5/b tan(30°)=b/5

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side. For angle $A = 30^{\circ}$ in right - triangle $ABC$, the opposite side to angle $A$ is $BC = 5$ cm and the adjacent side to angle $A$ is $AC=b$.
The formula for the tangent of an angle $\theta$ in a right - triangle is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Substitute values into the tangent formula

Substituting $\theta = 30^{\circ}$, opposite side $= 5$ cm and adjacent side $=b$ into the formula $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, we get $\tan(30^{\circ})=\frac{5}{b}$.

Answer:

$\tan(30^{\circ})=\frac{5}{b}$