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 solve the following problem. If ∠A
is 54 degrees and side a=430 mm
, then what is the length of side c to the nearest millimeter?

(1 point)
Responses

592 mm
592 mm

205 mm
205 mm

312 mm
312 mm

31 mm

Answer 1

B is 90°, so C = 90° − A = 36°. By the Law of Sines,
c / sin C = a / sin A → c = a * (sin C / sin A) = 430 * (sin 36° / sin 54°).

sin 36° ≈ 0.587785, sin 54° ≈ 0.809017 → c ≈ 430 * 0.726542 ≈ 312.4 mm.

To the nearest millimeter: 312 mm.