the angle of depression from a balloon on a 75-foot string to a person on the ground is 36degrees. how high is the balloon
Mathematics · Middle School · Sun Jan 24 2021
Answered on
Given the statement:
The angle of depression from a balloon on a 75-foot string to a person on the ground is 36degrees.
Determine the height of the balloon.
Solution:
The given problem represents a right triangle, whereas 75 is the value of the hypotenuse, and 36 degrees is the angle. In order to solve for the height, we apply the concept of SOH CAH TOA ( Sin = (Opposite/Hypotenuse), Cos = ( Adjacent/Hypotenuse), Tan = (Opposite/Adjacent) ). In our case, since we are asked for the height, we need to use Sin, since the height is opposite from the angle.
Sin = Opposite/Hypotenuse
Sin 36 = Height / 75
Multiply 75 on both sides of the equation, in order to cancel out the 75 in the deniminator.
(75) Sin 36 = Height / 75 (75)
Height = (75) Sin 36
Height = 44.08 ft
Final answer:
The height of the balloon is 44.08 ft.