Question

5. A student wants to know how tall the flagpole at her school is, her eye level is 5.5 feet above

the ground and she stands 36 feet from the base of the flagpole. If the angle of elevation is
25°, what is the height of the flagpole?

Answer 1

22.3 ft

Explanation:

Here we can make a triangle rectangle with the following vertex:

The student's eye level.

The top of the flagpole

The intersection between a horizontal line that passes through her eye level and a point in the flagpole.

The catheti of this triangle rectangle will be:

The distance between her and the flagpole (36ft)

The height of the flagpole minus the height of her eye level = H

We want to find the value of H.

We also know that the angle of elevation from her point of view is 25°.

(for this angle, the adjacent cathetus is the distance between her and the flagpole)

Now we can remember the relation:

Tan(a) = opposite cathetus/adjacent cathetus.

Then:

Tan(25°) = H/36ft

Solving for H we get:

Tan(25°)*36ft = H = 16.8 ft

And this is the height of the flag pole minus the height of her eye level, then the actual height of the flagpole is:

H + 5.5ft = 16.8 ft + 5.5ft = 22.3 ft