Question

which equation can be used to solve for b? triangle image with right angle at c, side cb = 5 cm, side ab = 10 cm, side ac = b, angle at a is 30° options: tan(30°) = 5/b; tan(30°) = b/5; tan(30°) = 10/b

Explanation:

Step1: Recall tangent definition

In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify sides for $\angle A = 30^\circ$

• Opposite side to $\angle A$: $BC = 5$ cm.
• Adjacent side to $\angle A$: $AC = b$ cm.

Step3: Apply tangent formula

$\tan(30^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{b}$.

Answer:

$\boldsymbol{\tan(30^\circ) = \frac{5}{b}}$ (the first option)