Question

A weather balloon is 529 meters above the ground. Two weather stations, A and B, monitor the balloon’s progress.

A weather balloon is 529 meters above the ground. Weather stations A and B are on the ground to form a triangle. A horizontal line is drawn at the top of the triangle to form angle v on the left and angle w on the right. The angle formed with A is x and the angle formed with B is y. A vertical line is drawn from the weather balloon to the ground to form a right angle and split the distance between A and B into 2 parts. The distance from A to the vertical line is 229 meters, and the distance between the vertical line and point B is 347 meters.

Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true? Check all that apply.

x > y
v > x
w = y
y < v
v = w
x < w

Answer 1

True statements:
- x > y
- w = y
- y < v

Reason: x = arctan(529/229) and y = arctan(529/347), so x > y because 229 < 347. The angles v and w are the angles of depression at the balloon and equal (by alternate interior angles / parallel horizontals) to the angles of elevation at A and B respectively, so v = x and w = y. From v = x and x > y we get y < v. The other statements are false.