The height of the balloon is 872 meters above the ground
Given, A meteorologist measures the angle of elevation to her weather balloon as 33 degrees.
A radio signal from the balloon indicates that it is 1601 meters diagonally from her location.
We have to find how high is the weather balloon above the ground?
We have to assume an right angle triangle here, with diagonal distance as hypotenuse and height of balloon as opposite side of elevation angle.
So, now, from above assumption,
Now, height of balloon = 1601 0.5446 = 871.967
Hence, the height of the balloon is 872 meters approximately.