If a pyramid’s height is 321, and the slant height is 436.5, what’s the length of the base? Round to nearest tenth
Let's use the Pythagorean theorem to find the length of the base. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the slant height) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height is one of the sides and the slant height is the hypotenuse. Let's call the length of the base "b."
The equation using the Pythagorean theorem is:
321^2 + b^2 = 436.5^2
103041 + b^2 = 190832.25
b^2 = 190832.25 - 103041
b^2 = 87791.25
Taking the square root of both sides, we get:
b = √87791.25
b ≈ 296.1
Therefore, the length of the base of the pyramid is approximately 296.1 when rounded to the nearest tenth.
No
I apologize for the previous incorrect response. Let's approach the problem correctly.
We can use the Pythagorean theorem to find the length of the base of the pyramid. The height, slant height, and base form a right triangle.
Using the Pythagorean theorem, we have:
Base^2 + Height^2 = Slant height^2
Let's substitute the given values into the equation:
Base^2 + 321^2 = 436.5^2
Base^2 + 103041 = 190832.25
Base^2 = 190832.25 - 103041
Base^2 = 87791.25
Taking the square root of both sides, we find:
Base ≈ √87791.25
Base ≈ 296.4 (rounded to the nearest tenth)
Therefore, the length of the base of the pyramid is approximately 296.4 when rounded to the nearest tenth.