Apply the Pythagorean Theorem to determine the height of the square pyramid Round the answer to the nearest tenth. the base is 40ft and the slant is 25ft. what is the height?
this ones for the quick check
1. 15.0
2. 59.5
3. 8.8
4. 9.1
5. 92.9
W person for giving answers
To apply the Pythagorean Theorem to find the height of the square pyramid, we need to use the formula:
a^2 + b^2 = c^2
where:
a is the height of the pyramid,
b is half the length of the base of the pyramid,
and c is the slant height of the pyramid.
Given:
Base length (b) = 40 ft
Slant height (c) = 25 ft
First, we need to find the value of half the base length (b). Since the base is a square, each side length is equal. Therefore, half the base length would be:
b = (1/2) * 40 ft = 20 ft
Now we can substitute the values into the Pythagorean Theorem:
a^2 + 20^2 = 25^2
Simplifying:
a^2 + 400 = 625
Subtracting 400 from both sides:
a^2 = 225
Taking the square root of both sides:
a = √225
a = 15 ft
Therefore, the height of the square pyramid is approximately 15 ft.
mitskilover tysm you just saved my grade-
To determine the height of the square pyramid using the Pythagorean Theorem, you will need to know the lengths of the base and the slant.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the slant is the hypotenuse, and the base and height form the other two sides of the right triangle.
Let's denote the height of the pyramid as h, the slant as s, and the base length as b.
According to the Pythagorean Theorem, we can write the equation as:
h^2 + (b/2)^2 = s^2
The base of the square pyramid is given as 40ft, so the length of one side of the base (since it's a square) would be 40ft as well.
Substituting the given values of b = 40ft and s = 25ft into the equation, we get:
h^2 + (40/2)^2 = 25^2
h^2 + 20^2 = 625
h^2 + 400 = 625
h^2 = 625 - 400
h^2 = 225
To solve for h, we take the square root of both sides:
h = √225
h = 15ft
Therefore, the height of the square pyramid is 15ft when rounded to the nearest tenth.
To summarize the steps:
1. Use the Pythagorean Theorem: h^2 + (b/2)^2 = s^2
2. Substitute the given values: h^2 + 20^2 = 25^2
3. Solve for h: h^2 = 225
4. Take the square root of both sides: h = √225
5. Round the answer to the nearest tenth: h ≈ 15ft
lets goo. thx @mitskilover!!
TUSM!! @mitskilover
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