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A granular substance such as sand naturally settles into a cone-shaped pile when poured from a small aperture. Its height depends on the humidity and adhesion between granules. The angle of elevation of a pile, θ, is called the angle of repose. If the height of a pile of sand is 15 feet and its diameter is approximately 52 feet, determine the angle of repose. Round answer to nearest degree.

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Answer:

The angle of elevation of the pile is 30°

Step-by-step explanation:

Given that;

Height = 15 ft

Diameter = 52 ft

so radius r = D/2 = 52/2 = 26 ft

Now, to get the angle of elevation.

given the details in the question,

we can say; the given height is the opposite which is 15 ft.

Also the radius is adjacent which is 26 ft

using SOH CAH TOA

TOA; Tan = Opposite / Adjacent

so

tan∅ = 15 ft / 26 ft

tan∅ = 0.5769

∅ = tan⁻¹( 0.5769 )

∅ = 29.98° ≈ 30°

Therefore, The angle of elevation of the pile is 30°

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