A car travels along a straight road, heading east for 1 h, then traveling for 30 min on another road that leads northeast.

Question

A car travels along a straight road, heading east for 1 h, then traveling for 30 min on another road that leads northeast. If the car has maintained a constant speed of 40 mi/h, how far is it from its starting position? (Round your answer to one decimal place.)

??? mi

Answer 1

This problem can be solved in several ways. This ways requires familiarity with the Law of Cosines:

c² = a² + b² - 2*a²*b²*cos(C)

a = distance traveled due east for 1 hour at 40 mph = 40 mi

b = distance traveled north-east for 30 min at 40 mph = 20 mi

C = the angle between the two segments = 135^o.

Angle C requires some explanation. Turning from due-East to north-east requires a 45^o turn. But this angle is exterior angle to the triangle formed by these two segments. The Law of Cosines requires the use of the interior angle that is opposite to the unknown side. That angle is simply 180 - 45 = 135.

c² = a² + b² - 2*a²*b²*cos(C) = (40)² + (20)² - (2)(40)(20)*cos(135^o) = 3131.4

c = sqrt(3131.4) = 55.959 mi

Ans: 56.0 mi