The angle of elevation of a weather balloon is 41 degrees. The balloon is 1503m from his location. How high above the ground is the balloon

Question

A meteorologist measures the angle of elevation of a weather balloon as 41 degrees. A radio signal from the balloon indicates that it is 1503 meters from his location. To the nearest meter, how high above the ground is the balloon?

Answer 1

Draw a right triangle with one leg representing the ground. The balloon is at the vertex above the right angle. Assume the meteorologist is on level ground and positioned at the other vertex. The distance between the meteorologist and the balloon is the hypotenuse r and the angle between the ground and the hypotenuse is θ.  Label the distance of leg from the ground to the balloon y.  The quantities are related by y/r = sin(θ). Solve for y, substitute in the numbers and calculate y, which is units of meters.

 

The problem does not state if the meteorologist is on the level ground or above or below ground level. So you should clearly state your assumption, namely "Assume the meteorologist is on level ground."