A tent manufacturer designs a tent in the shape of a cone. The slant height of the cone is 4 m and the radius of the base is 2.5 m. Calculate the angle between the slant height and the base of the tent.

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Question

A tent manufacturer designs a tent in the shape of a cone. The slant height of the cone is 4 m and the radius of the base is 2.5 m. Calculate the angle between the slant height and the base of the tent.

Accepted Answer

51.3° — 3°. Award 1 mark for the method and 1 mark for the answer. The angle between the slant height and the base is found from the radius and the slant height: cos θ = r ÷ l = 2.5 ÷ 4 = 0.625, so θ = cos⁻¹(0.625) = 51.3° to one decimal place. The value 38.7° is the angle between the slant height and the vertical axis, which is the complement of the required angle. The values 32.0° and 58.0° do not follow from either ratio.

Answer

32.0°

Answer

58.0°

Answer

51.3°

Answer

38.7°

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