A meteorologist measures the angle of depression of a weather balloon as 53". A radio signal from the balloon indicates that it is 1680 feet from his receiver. How high is the weather balloon from the ground?

Answer 1

We can solve the problem with the help of trigonometry. Let's denote the height of the weather balloon from the ground as "h" and the distance between the meteorologist and the balloon as "d".

Since we know the angle of depression, we also know that the angle between the ground and the line of sight to the balloon is also 53 degrees (because the sum of angles in a triangle is 180 degrees).

Now we can use the tangent function to find the height of the balloon:

tan(53 degrees) = h / 1680 feet

Solving for h, we get:

h = 1680 feet * tan(53 degrees)

h ≈ 2019.78 feet

Therefore, the weather balloon is approximately 2019.78 feet high from the ground.