The Great Pyramid of Cheops has a square base with a length

The Great Pyramid of Cheops has a square base with a length of 756 feet. Its height is 482 feet. If you walk straight up from the center of the north side to the top of the pyramid you have to climb an angle of ______ degrees.
You decide to simplify your life and walk up along one of the ridges. Thus you have to climb only at an angle of _______degrees.
On your way up the ridge you walk a distance of______ feet.
Hint: For the first two parts draw right triangles and use an inverse trig function. For the third part just use the Pythagorean Theorem

Solution

given that square base with a length of 756 feet. Its height is 482 feet

1) Right triangle from face has height = 482 ft,

base = 756/2 = 378 ft.
Tan(angle) = 482/378.

Therefore, angle = arctan(482/378)

= 51.9º.

2) Right triangle from ridge has height = 482 ft.

Base is hypotenuse of right triangle with both legs = 756/2 = 378 ft.

Thus, base = sqrt(378^2 + 378^2) = sqrt(2*378^2).

Tan(angle) = 482/sqrt(2*378^2).

Therefore, angle = arctan[482/sqrt(2*378^2)] = 42.0º.

3) ridge length = sqrt(height^2 + base^2)

= sqrt(482^2 + 2*378^2)

= 720 ft.