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 ∠A=55 degrees
∠
𝐴
=
55

degrees
and side a=450 km
𝑎
=
450

km
, then find the length of side c to the nearest kilometer.

(1 point)
km

Answer 1

Using the Law of Sines: c/sin C = a/sin A. Here B = 90°, so C = 180° − 90° − 55° = 35°. Thus

c = a * (sin 35° / sin 55°) = 450 * (sin 35° / sin 55°) ≈ 450 * 0.70021 ≈ 315.09 km.

To the nearest kilometer: 315 km.