Question

which equation can be used to solve for b?
(there is a right triangle abc with right angle at c. side bc is 5 cm, side ab is 10 cm, side ac is b, and angle at a is 30°.)
options:

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

Explanation:

Step1: Identify sides for angle A

For $\angle A = 30^\circ$, opposite side is $BC = 5$ cm, adjacent side is $AC = b$.

Step2: Recall tangent definition

Tangent of an angle is $\frac{\text{opposite}}{\text{adjacent}}$.

Step3: Substitute values

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

Answer:

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