84.1k views
5 votes
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

1 Answer

2 votes

Final answer:

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.

User Sergey Morozov
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories