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.

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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