What is the slant height x of this square pyramid? The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge and is labeled as x. The length of the lateral edge is 4 meters. The lateral edge makes a 60 degree angle with the base edge. Enter your answer in the box. Express your answer in radical form.

Question

Mathematics

Ross

28 December, 05:59

What is the slant height x of this square pyramid? The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge and is labeled as x. The length of the lateral edge is 4 meters. The lateral edge makes a 60 degree angle with the base edge. Enter your answer in the box. Express your answer in radical form.

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Answers (1)

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Julia Fisher · Answer 1

The side adjacent to the 60° angle in the right triangle consisting of x, the lateral edge, and half the base edge is half the base edge, 2 m. The side opposite that angle is x. Thus you have

tan (60°) = x / (2 m)

(2 m) * tan (60°) = x = 2√3 m

The slant height is 2√3 meters.