Trigonometry: Right Angle homework

Question

A truck leaves its present location and travels along a bearing of S33 degreesE  for 57 miles.

How far South and East of its original position is it? Round your answers to two decimal places.

A truck leaves its present location and travels along a bearing of N42degreesW for 40 miles.

How far North and West of its original position is it? Round your answers to two decimal places.

Answer 1

S33 degreesE is 33° from South in the direction of East.

∠ is 33º.

y = 57 • cos(33°) = 47.8

x = 57 • sin(33°) = 31.04

Answer 2

57/sin90 = a/sin33

57sin33 = asin90

a = 57sin33

a = 31.04 miles east

31.04² + b² = 57²

b² = 57² - 31.04²

b = √(57² - 31.04²)

b = 47.81 miles south