Answer:
22.3 ft
Step-by-step 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
