An airplane is flying from City A to City B at a bearing of 100°. The distance between the two cities is 1,200 miles. How far west is City A relative to City B?
Round the answer to the nearest mile.

Use the following graph to set up and solve the problem. Let the origin be City A. The perpendicular symbol around the origin is assumed and has been removed.

A) Set up the problem by adding the given information to the graph.
Given information: the bearing and the distance between two cities

B) Fill in the rest of the needed information onto the graph.
Needed information: the unknown angle measure and unknown distance

C) Analyze the completed figure to make the following calculations.
1. Calculate the needed angle measure.

2. Calculate the needed distance.

D) Write your answer in a complete sentence

A) Let's add the given information to the graph. City A is represented by the origin, and we know that the airplane is flying at a bearing of 100° from City A to City B.

B) Now, we need to fill in the rest of the information. We have the unknown angle measure and the unknown distance.

C) Analyzing the completed figure, we can make the following calculations:
1. To find the needed angle measure, we subtract 100° from 180° (since the angle formed by the perpendicular symbol and the line connecting City A to City B is a right angle).
180° - 100° = 80°

2. To calculate the needed distance, we can use trigonometry. Since the distance between the two cities is the hypotenuse of a right triangle, and the angle opposite the distance is 80°, we can use the sine function:
sin(80°) = opposite/hypotenuse
sin(80°) = distance/1,200 miles

Solving for the distance:
distance = sin(80°) * 1,200 miles

D) In a complete sentence, the answer is: City A is approximately 1,153 miles west of City B. ️