Final answer:
The height of the flagpole can be determined by using the tangent trigonometric ratio of the given angle of elevation (36 degrees) and the length of the shadow (40 feet). The flagpole is approximately 29.06 feet tall.
Step-by-step explanation:
To solve the problem of finding the height of the flagpole given the shadow length and the angle of elevation, we can use trigonometric ratios. Specifically, the tangent function relates the angle of elevation to the opposite side (height of the flagpole) and the adjacent side (length of the shadow). The angle of elevation is given as 36 degrees and the length of the shadow is 40 feet.
The tangent of the angle is the ratio of the opposite to the adjacent side, so we can write the equation:
tan(36°) = height / 40 ft
Solving for the height, we get:
height = 40 ft * tan(36°)
Using a calculator, we find:
height = 40 ft * 0.7265
height = 29.06 ft
Therefore, the flagpole is approximately 29.06 feet tall.