Question

which equation can be used to solve for b?
triangle with right angle at c, angle at b is 30°, side bc is 8 ft, side ac is b
options:

• ( b = (8)\tan(30^circ) )
• ( b = \frac{8}{\tan(30^circ)} )
• ( b = (8)sin(30^circ) )
• ( b = \frac{8}{sin(30^circ)} )

Explanation:

Step1: Identify sides relative to 30°

In right triangle $ABC$, $\angle B=30^\circ$, adjacent side to $\angle B$ is $8$ ft, opposite side is $b$.

Step2: Use tangent trigonometric ratio

Recall $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. Substitute values:
$\tan(30^\circ)=\frac{b}{8}$

Step3: Rearrange to solve for $b$

Multiply both sides by 8:
$b=(8)\tan(30^\circ)$

Answer:

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