Question

Apyramid was built about 2570 BC. Its original height was 453 feet, 11 inches, but

due to loss of its topmost stones, it is now shorter. Find the current height of the
pyramid, using the information given in the fiqure on the right.
48.85€
The current height of the pyramid is feet
(Do not round until the final answer. Then round to two decimal places as needed.).​

Answer 1

422.44

Explanation:

Answer 2

422.44 feet

Explanation:

Let A, B, X, and H represent the left-most observation point, the observation point to its right, the point immediately below the apex, and the height of the apex, respectively.

Then the definition of the cotangent function tells us ...

AX = H·cot(42°)

BX = H·cot(48.85°)

Since the figure tells us AB = 100 feet, we have ...

AB = AX -BX

100 = H·cot(42°) -H·cot(48.85°)

H = 100/(cot(42°) - cot(48.85°)) ≈ 422.44 . . . . ft

The current height of the pyramid is 422.44 feet.