Question

Donna is standing 123 feet from the base of a flagpole. She uses a smartphone app to measure the angle of elevation from eye-level to the top of the pole, and she finds the angle to be 26º. If her eyes are 5.3 feet above the ground, find the total height of the flagpole.

a) 117.7 feet
b) 124.3 feet
c) 128.6 feet
d) 133.3 feet

Answer 1

The total height of the flagpole measured from the ground and based on the provided angle of elevation and distance is approximately 65.2 feet. This result does not match any of the provided options (a, b, c, or d).

Step-by-step explanation:

Finding the Height of the Flagpole

To find the total height of the flagpole given the angle of elevation and the distance from the flagpole to Donna's position, we can use trigonometry. The tangent of the angle of elevation (θ) is equal to the opposite side (height of the flagpole above Donna's eye level) over the adjacent side (distance from Donna to the base of the flagpole).

Step-by-Step Calculation

1. Use the formula tan(θ) = opposite/adjacent.
2. Plug in the values: tan(26°) = height/123 feet.
3. Multiply both sides by 123 feet to solve for the height above her eye level.
4. Add Donna's eye level height to find the total height.

The calculation is as follows:

• tan(26°) ≈ 0.4877
• So, 0.4877 = height/123
• height = 0.4877 * 123 feet
• height ≈ 59.9 feet above her eye level
• Total height = 59.9 feet + 5.3 feet
• Total height ≈ 65.2 feet (not matching any of the options provided)

None of the options a) 117.7 feet, b) 124.3 feet, c) 128.6 feet, or d) 133.3 feet correctly describe the height of the flagpole based on the given angle of elevation and distance.