Question

The measure of angle A is 15°, and the length of side BC is 8. What are the lengths of the other two sides, rounded to the nearest tenth?

A. \(BC = 8, AB \approx 2.6, AC \approx 7.9\)

B. \(BC = 8, AB \approx 7.9, AC \approx 2.6\)

C. \(BC = 8, AB \approx 6.9, AC \approx 7.9\)

D. \(BC = 8, AB \approx 7.9, AC \approx 6.9\)

Answer 1

To find the lengths of the other two sides, use the trigonometric functions sine and cosine. AB is approximately 2.6 and AC is approximately 7.9.

Step-by-step explanation:

To find the lengths of the other two sides, we can use the trigonometric functions sine and cosine. We know that angle A is 15° and the length of side BC is 8. To find side AB, we can use the sine function:

sin(15°) = AB / 8

AB = 8 * sin(15°) = 2.6 (rounded to the nearest tenth)

To find side AC, we can use the cosine function:

cos(15°) = AC / 8

AC = 8 * cos(15°) = 7.9 (rounded to the nearest tenth)