Question

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=28 degrees
∠
𝐶
=
28

degrees
and side c=28 m
𝑐
=
28

m
, then what is the length of side a to the nearest meter?

(1 point)
Responses

25 m
25 m

62 m
62 m

15 m
15 m

53 m
53 m

Answer 1

Because the side labeled b is the hypotenuse, angle B = 90°, so A = 90° − 28° = 62°. By the Law of Sines,
a/sin(A) = c/sin(C) ⇒ a = c·sin(A)/sin(C) = 28·sin(62°)/sin(28°) ≈ 52.66 m.
Rounded to the nearest meter: 53 m.