You are holding one of the tethers attached to the top of a giant character balloon in a parade.Before the start of the parade the balloon is upright and the bottom is floating approximately 20 feet above ground level.You are standing approximately a = 100 feet ahead of the balloon (see figure).Round your answer to two decimal places. Find the height h of the balloon if the angle of elevation to the top of the balloon is 35º.

A)55.02 ft
B)56.02 ft
C)53.02 ft
D)57.02 ft
E)54.02 ft

Question

You are holding one of the tethers attached to the top of a giant character balloon in a parade.Before the start of the parade the balloon is upright and the bottom is floating approximately 20 feet above ground level.You are standing approximately a = 100 feet ahead of the balloon (see figure).Round your answer to two decimal places.​  ​ Find the height h of the balloon if the angle of elevation to the top of the balloon is 35º.
​
A)55.02 ft 
B)56.02 ft 
C)53.02 ft 
D)57.02 ft 
E)54.02 ft

Quizplus · Accepted Answer

We can use trigonometry to solve the problem.

Let h be the height of the balloon above the ground level (the distance we're looking for). Also, let d be the horizontal distance between the person holding the tether and the base of the balloon.

From the figure, we have:

tan(35º) = h/d 
d = a + 20

Substituting d in the first equation, we get:

tan(35º) = h / (a + 20)

Multiplying both sides by a + 20, we get:

h = (a + 20) tan(35º)

Substituting a = 100, we obtain:

h = (100 + 20) tan(35º) ≈ 53.02 ft

Therefore, the answer is C) 53.02 ft.

You Are Holding One of the Tethers Attached to the Top