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?
To find the height of the weather balloon, we can use trigonometry.
Let the height of the weather balloon be h feet.
Since the angle of depression is 53°, the angle of elevation from the ground to the weather balloon is also 53°.
This forms a right triangle with the height of the weather balloon as the opposite side and the distance from the receiver to the weather balloon (1680 feet) as the adjacent side.
Using the tangent function, we have:
tan(53°) = opposite/adjacent
tan(53°) = h/1680
Now, we can solve for the height of the weather balloon:
h = 1680 * tan(53°)
h = 1680 * 1.3
h ≈ 2184 feet
Therefore, the weather balloon is approximately 2184 feet high from the ground.