find the height of a pyramid whose square base measures 30yd on each side and whose slant height it 45yd?
Pythagorean Theorem.
15^2 + h^2 = 45^2
225 + h^2 = 2,025
h^2 = 1800
h = 42.4 yards
A blue water tank with a diameter of 4 meters and a height of 6 meters
To find the height of the pyramid, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the slant height acts as the hypotenuse, and the height and the base form the other two sides of a right-angled triangle.
Let's denote the height of the pyramid as 'h', the slant height as 'l', and the base as 'b'.
We are given that:
b = 30 yd
l = 45 yd
Using the Pythagorean theorem, we can write the equation as:
l^2 = h^2 + b^2
Substituting the given values:
45^2 = h^2 + 30^2
2025 = h^2 + 900
Rearranging the equation to solve for 'h':
h^2 = 2025 - 900
h^2 = 1125
Taking the square root of both sides:
h = √1125
h ≈ 33.54
Therefore, the height of the pyramid is approximately 33.54 yards.
To find the height of a pyramid, you can use the Pythagorean theorem and the formula for the slant height (lateral height).
1. First, let's represent the given information:
- The length of the base of the pyramid: 30 yards
- The slant height (lateral height) of the pyramid: 45 yards
2. With this information, we can form a right triangle with the slant height as the hypotenuse, the height (h) as one of the legs, and half the base length (15 yards) as the other leg.
3. Using the Pythagorean theorem, we can determine the height (h) of the pyramid:
h^2 + 15^2 = 45^2
h^2 + 225 = 2025
h^2 = 2025 - 225
h^2 = 1800
4. Simplifying further:
h = √1800
h ≈ 42.43 yards
Therefore, the height of the pyramid is approximately 42.43 yards.