Question

Please help me! Thank you!

Answer 1

Answer:

B

Step-by-step explanation:

Since we know the measure of ∠B and the side opposite to ∠B and we want to find BC, which is adjacent to ∠B, we can use the tangent ratio. Recall that:

$\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}$

The angle is 54°, the opposite side measures 16 units, and the adjacent side is BC. Substitute:

$\displaystyle \tan 54^\circ = \frac{16}{BC}$

Solve for BC. We can take the reciprocal of both sides:

$\displaystyle \frac{1}{\tan 54^\circ} = \frac{BC}{16}$

Multiply:

$\displaystyle BC = \frac{16}{\tan 54^\circ}$

Use a calculator. Hence:

$\displaystyle BC \approx 11 .62\text{ units}$

BC measures approximately 11.62 units.

Our answer is B.