the great pyramid of cheops is a square based pyramid with a height of 147 meters and a base length of 230 meters. find the angle to the nearest degree that one of the edges of the pyramid makes with the base

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  1. (I don't have my calculator with me, so I will describe the method)

    - find the length of the diagonal of the base using Pythagoras
    - take half of that length (the midpoint of the base)
    - use tan^-1 (147/half-length of diagonal)

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  2. the base of the 52 degrees triangle is half of the base of the pyramid (so in this case 115 m) Using simple trig ratios, solve for the height of the pyramid (tan 52 = x/115, x= 147.2m). Now to find the other side of the triangle do pythagorean theorem on the square base to find the diagonal and divide that by 2. (230^2 + 230^2 = c^2, c = 325.269 m) 325.269 / 2 = 162.635m. Now you have the two sides of the triangle and using the tangent ratio, solve for the angle, you should get 47.8 degrees.

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