Question

A helium-filled balloon is attached to a 100 m long string. The string is tied to a hook on the ground and it makes an angle of 60° with the ground, as shown below.

The figure shows a right angle triangle with a balloon at the tip of the triangle. The string attached to the balloon makes an angle of 60 degrees to the ground. The length of the string is 100 meters.

What is the height of the balloon from the ground?
Answer

50 m

86.6 m

70.72 m

100 m

Answer 1

height / 100 = sin 60
height = 86.6

Answer 2

You can get the same answer as above if you remember your unit circle points:
pi/3 radians on the unit circle is (1/2,sqrt3/2). The sqrt3/2 (times 100) is your 87 percent answer.