Question

After a wind storm, you notice that your 17-foot flagpole may be leaning. From a point on the ground 14 feet from the base of the flagpole, you find that the angle of elevation to the top is 52°. Is the flagpole leaning? If so, find the acute angle, to the nearest degree, that the flagpole makes with the ground.

A. Yes, 38°
B. No, 52°
C. Yes, 52°
D. Yes, 48°

Answer 1

Yes, the flagpole is leaning. The acute angle that the flagpole makes with the ground is approximately 48°.

Step-by-step explanation:

Yes, the flagpole is leaning. To find the acute angle that the flagpole makes with the ground, we can use trigonometry. Since we have the angle of elevation to the top of the flagpole and the distance from the base to the point on the ground, we can use the tangent function to calculate the angle the flagpole makes with the ground.

Tan(angle) = Opposite/Adjacent

Tan(52°) = x/14

x ≈ 14 * Tan(52°) ≈ 14 * 1.2799 ≈ 17.92

The flagpole is leaning approximately 17.92 feet from the vertical. Therefore, the acute angle that the flagpole makes with the ground is approximately 17.92 feet. So the correct answer is: (D) Yes, 48°.