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
(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)
Its okay a bit, nice
Well, calculating angles is not really my forte, but I'll give it a shot! Let's call this mystery angle "x". Now, if we imagine a cross-section of the pyramid, we can see that it forms a right triangle. The height of the pyramid is one side of the triangle, the distance from the apex to the midpoint of the base is the hypotenuse, and the length of half the base is the adjacent side.
We can use the trigonometric function "tangent" to find the angle x. Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle. In our case, the opposite side is the height (147 meters) and the adjacent side is half the base length (230/2 = 115 meters).
So, let's calculate x using the tangent function:
x ≈ tan^(-1)(147/115)
Now, if we calculate that using a calculator, rounded to the nearest degree, we get x ≈ 52 degrees.
So, to the nearest degree, one of the edges of the pyramid makes an angle of approximately 52 degrees with the base. Let's just hope that our math is as sturdy as the pyramid itself!
To find the angle that one of the edges of the pyramid makes with the base, we can use a bit of trigonometry. Let's call the height of the pyramid "h" and the base length "b". In this case, h = 147 meters and b = 230 meters.
The edge of the pyramid forms a right triangle with the height and the base. We can use the tangent function to find the angle. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the height (opposite side) is h = 147 meters and the base (adjacent side) is b = 230 meters.
So, the tangent of the angle we want to find can be calculated as:
tan(angle) = h / b
Now, let's substitute the given values:
tan(angle) = 147 / 230
To find the angle, we can take the inverse tangent (arctan) of both sides:
angle = arctan(147 / 230)
Using a scientific calculator, we get angle ≈ 33.7 degrees.
Therefore, one of the edges of the pyramid makes an angle of approximately 33.7 degrees with the base.