Question

A conical circus tent has a 20 ft central pole that supports it. The slant height of the tent is 26 ft long. Explain how to find the angle the tent pole makes with the sides of the tent. A diagram of a cone. The length and height of a cone are 26 feet and 20 feet. The central pole forms a right triangle with the floor of the tent. The of the missing angle is the ratio of the length of the central pole to the length of the side of the tent, which is . Applying , we find that the angle the tent pole makes with the sides of the tent is .

Answer 1

The angle the tent pole makes with the sides of the tent is 39.7°

Applications of Trigonometry

From the question, we are to determine the angle the tent pole makes with the sides of the tent

Let the angle be θ

Using SOH CAH TOA

Thus,

cos θ = Adjacent/Hypotenuse

The adjacent corresponds to height of the central pole

and the slant height of the tent is the hypotenuse

∴ Adjacent = 20 ft

Hypotenuse = 26 ft

Thus,

cos θ = 20 / 26

cos θ = 0.76923

∴ θ = cos⁻¹(0.76923)

θ = 39.7°

Hence, the angle the tent pole makes with the sides of the tent is 39.7°

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