Question

A commuter plane flies from City A to City B, a distance of 90 mi due

north. Due to bad weather, the plane is redirected at take-off to a
heading N 60° W (60° west of north). After flying 57 mi, the plane is
directed to turn northeast and fly directly toward City B. To the
nearest tenth, how many miles did the plane fly on the last leg of
the trip?

1. Based on the diagram provided for this problem, which measures of the triangle do you know?
2. What are the values of these measures?
3. Describe the part of the triangle you need to find.
4. What concept will you use to write an equation? What is the equation?
5. Solve the equation. What is the distance of the last leg of the trip?

Answer 1

The triangle in the diagram has two known adjacent sides (57 mi and 90 mi) and angle between these sides (60°), so you can use the cosine theorem to find the opposite side to the known angle. Denote unknown side as a, then:

`a^2=57^2+90^2-2\cdot 57\cdot 90\cdot \cos 60^(\circ), \\\\a^2=3249+8100-10260\cdot (1)/(2) ,\\ \\ a^2=11349-5130,\\a^2=6219,\\a=78.86063656\approx 78.9` mi.

Answer: the distance of the last leg of the trip is 78.9 mi.