Question

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Right triangle upper A upper B upper C has a small square box at angle B. The side opposite of each angle is labeled as the lowercase letter of the angle name.
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Use the Law of Sines to find the length of side c, to the nearest millimeter, if ∠A=72 degrees
and side a=1,246 mm
.

(1 point)
Responses

3,835 mm
3,835 mm

385 mm
385 mm

405 mm
405 mm

366 mm

Answer 1

Angle B = 90°, so C = 180° − 90° − 72° = 18°.

By the Law of Sines: c = a * sin C / sin A = 1246 * sin(18°) / sin(72°).

Compute: sin(18°) ≈ 0.309017, sin(72°) ≈ 0.951057
c ≈ 1246 * 0.309017 / 0.951057 ≈ 404.9 mm ≈ 405 mm.

Answer: 405 mm.