Question

Please help me! Thank you!

Find the length of BC
A. 27.22
B. 11.62
C. 22.02
D. 19.78

Answer 1

B

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 = (16)/(BC)`

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

`\displaystyle (1)/(\tan 54^\circ) = (BC)/(16)`

Multiply:

`\displaystyle BC = (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.