The present height of the pyramid of Khafre in Egypt is 137m.An engineer surveying pyramid measures an angle of elevation of 33degrees from a point X to the top of the pyramid. Calculate the distance from X to the cenre of the base of the pyramid at Y

Assuming the point X is on ground which is level with the base of the pyramid, this would be just a case of

finding the distance d, where
tan33° = 137/d or
d = 137/tan33° m

To calculate the distance from point X to the center of the base of the pyramid at point Y, we need to use trigonometry. Specifically, we will be using the tangent function, as we have the angle of elevation and the height of the pyramid.

Let's label the unknown distance from X to Y as "d".

1. Draw a diagram: Draw a right triangle where the height of the pyramid (137m) is the opposite side, and the unknown distance (d) is the adjacent side to the angle of elevation. Label the angle of elevation as θ.

^
|\
| \
| \ 137m
| \
X ____|____\ Y
d

2. Use the tangent function: In a right triangle, the tangent of an angle is equal to the ratio of the length of the opposite side to the adjacent side. In this case, we have:

tan(θ) = opposite/adjacent

Rearrange the equation to solve for the adjacent side (d):

d = opposite/tan(θ)

3. Plug in the values: Let's substitute the values we have into the equation. The opposite side is the height of the pyramid (137m), and the angle of elevation (θ) is 33 degrees.

d = 137m / tan(33°)

4. Calculate the distance:

Using a scientific calculator, find the tangent of 33 degrees. Multiply this result by 137 meters. The resulting value will be the distance from X to Y.

d ≈ 233.71 meters

Therefore, the distance from point X to the center of the base of the pyramid at point Y is approximately 233.71 meters.