Question

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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The adjacent side, from angle upper A to angle upper B, is labeled as lowercase c. The hypotenuse, from angle upper A to angle upper C, is labeled as lowercase b. The opposite side, from angle upper B to angle upper C, is labeled as lowercase a.

Use the Law of Sines to solve the following problem. If ∠C=62 degrees
and side c=16 cm
, then what is the length of side a? Round your answer to the nearest centimeter.

(1 point)
cm
Remaining Attempts : 3
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Answer 1

Angle A = 180° − 90° − 62° = 28°. By the Law of Sines,
a/sin A = c/sin C, so
a = c * sin A / sin C = 16 * sin28° / sin62°.

Since sin62° = cos28°, this equals 16·tan28° ≈ 16·0.531709 = 8.51 cm,
which rounds to 9 cm.