Geometry Proof - Thanks for the help

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

A is the starting point.

B is the turning point.

C is the city.

AC is due north (a vertical line) with measure 90 miles

AB is 57 miles.

Angle CAB is 60.

BC is the side measure that we need to find.

The law of cosines shall be used to solve the problem

x^2 = 57^2 + 90^2 - 57*90 cos60

x^2 = 3249 + 8100 - 2565

x^2 = 8784

x = 93.7