If you were to climb the pyramid from base to top, what distance along the face of the pyramid would you travel?

Question

The Great Pyramid of Giza is 139 meters tall, with a slope of 51.8 degrees. If you were to climb the pyramid from base to top, what distance along the face of the pyramid would you travel?

Answer 1

If you look at the triangle made by the pyramid's height, one of the edges (which you would climb) and the line that connects on the ground the base of the height and the start of the edge, you will get a right triangle, where the height is an leg; the line on the ground connecting the base of the height and the start of the edge is a leg, and the edge you want to climb is the hypotenuse. Using the information you have, you can now see that the angle between the leg on the ground and the pyramid's edge form a 51.8 degree angle, and the opposite leg, aka the height of the pyramid is 139 meters. So in a right triangle you are given an angle and the length of the opposite leg, and you have to find out the length of the hypotenuse, aka your edge (or climbing path).

cos(51.8) = height/hypotenuse, from here hypotenuse = height/cos(51.8)

make sure to use degrees on your calculator, not radians