Question

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

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. In right - triangle $ABC$ with right - angle at $C$, for angle $A = 30^{\circ}$, the side opposite to angle $A$ is $BC = 5$ cm and the side adjacent to angle $A$ is $AC=b$.

Step2: Apply the tangent formula

Using the formula $\tan(A)=\frac{\text{opposite}}{\text{adjacent}}$, and substituting $A = 30^{\circ}$, $\text{opposite}=5$ cm and $\text{adjacent}=b$, we get $\tan(30^{\circ})=\frac{5}{b}$.

Answer:

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