Question

When the angle of elevation to the sun is 26°, a flagpole casts a shadow that is 82 feet long. What is the height of the flagpole to the nearest foot?

a) 30 feet
b) 50 feet
c) 85 feet
d) 100 feet

Answer 1

To find the height of the flagpole, we use the tangent of the angle of elevation (26°) and the length of the shadow (82 feet). The calculation shows that the flagpole is approximately 40 feet tall, which rounds to the nearest available option, (b) 50 feet.

Step-by-step explanation:

The student asked about determining the height of a flagpole given the length of its shadow and the angle of elevation to the sun. To solve this, we can use trigonometric functions. With an angle of elevation of 26° and a shadow length of 82 feet, the tangent function in a right-angled triangle will be useful here. The formula is tan(\theta) = opposite/adjacent.

Let h be the height of the flagpole, so:

tan(26°) = h / 82 feet

Multiplying both sides by 82 feet, we get:

h = 82 feet × tan(26°)

Calculating this gives the height of the flagpole as:

h ≈ 82 feet × 0.4877 ≈ 40 feet

To the nearest foot, the height of the flagpole is approximately 40 feet, which is not listed in the multiple-choice options, but closest to 50 feet. Therefore, the correct answer from the given options is (b) 50 feet.