Question

A flag is flying at the top of a flagpole. The flagpole casts a shadow of 21 feet along the ground. The angle of the sun shining down (the angle of depression) is 66°. How tall is the flagpole?

a) 19.07 feet
b) 31.09 feet
c) 24.55 feet
d) 15.12 feet

Answer 1

The correct answer is option (c) 24.55 feet.To find the height of the flagpole, we use trigonometry, specifically the tangent function of the angle of elevation, which is 66°.

Step-by-step explanation:

To solve the problem, we need to apply trigonometry. With a 66° angle of depression, the angle of elevation from the ground to the top of the flagpole is also 66°, since alternate interior angles of parallel lines cut by a transversal are congruent. It forms a right triangle with the ground and the pole. The shadow is the adjacent side, and the height of the flagpole is the opposite side. We use the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle. Therefore, tangent of 66° = height / 21 feet. The height can be found by multiplying the tangent of 66° by 21 feet, which gives us the height of the flagpole.

Mathematically, it's:

height = 21 feet × tan(66°)
≈ 21 feet × 2.246
≈ 47.17 feet

But, remember to keep your calculator in degree mode since the angle is given in degrees.