how many miles long is the base of the pyramid? the height is 35mi and the slant is 37mi the base of the square pyramid is how many feet long?
To calculate the length of the base of the pyramid, we need to apply the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides (height and half the base length).
Let's denote the height as h = 35 mi, the slant height as s = 37 mi, and the base length as b. We'll also denote r as half the base length.
Using the Pythagorean theorem, we have:
s^2 = h^2 + r^2
Plugging in the given values:
37^2 = 35^2 + r^2
Simplifying:
1369 = 1225 + r^2
Subtract 1225 from both sides:
r^2 = 144
To find the base length (b), we simply double the value of r:
b = 2r
b = 2 * √144
b = 2 * 12
b = 24 mi
To convert the base length from miles to feet, we know that 1 mile is equal to 5280 feet. So to get the length in feet, we multiply the base length in miles by 5280:
base length in feet = 24 mi * 5280 ft/mi
base length in feet = 126,720 ft
Therefore, the base of the pyramid is 24 miles long and 126,720 feet long.
To find the length of the base of the pyramid, we can use the Pythagorean theorem, which 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 other two sides.
Let's denote the base length of the square pyramid as "b". We have the height (h) as 35 miles and the slant height (s) as 37 miles.
Using the Pythagorean theorem, we can determine the length of the base as follows:
The equation for the Pythagorean theorem is:
s^2 = h^2 + b^2
Plugging in the values we have:
37^2 = 35^2 + b^2
Simplifying, we get:
1369 = 1225 + b^2
Next, we can isolate the term with b^2:
b^2 = 1369 - 1225
b^2 = 144
Taking the square root of both sides, we find:
b = √144
b = 12
Therefore, the base length of the square pyramid is 12 miles.
Now, if you want to convert the base length to feet, you need to know that there are 5,280 feet in a mile. Multiplying the base length in miles by this conversion factor will give you the base length in feet:
Base length in feet = 12 miles * 5,280 feet/mile
Base length in feet = 63,360 feet
So, the base of the square pyramid is 63,360 feet long.
To calculate the length of the base of a pyramid, you can use the Pythagorean theorem. In this case, we have the height and the slant height, so we can find the length of the base.
Let's use the Pythagorean theorem equation:
(a^2) + (b^2) = (c^2)
Here, a and b are the two sides of the base, and c is the slant height.
Let's solve for a (one of the sides of the base):
a^2 + (35^2) = (37^2)
a^2 + 1225 = 1369 (taking the square of 35 and 37)
a^2 = 1369 - 1225 = 144
Taking the square root of both sides:
a = √144 = 12
So, the length of one side of the base is 12 miles.
Since the pyramid is square-based, all sides are equal in length. Therefore, the length of the base is 12 miles.
To convert this length to feet, we multiply it by 5280 (since 1 mile is equal to 5280 feet):
12 miles x 5280 feet/mile = 63,360 feet.
So, the base of the square pyramid is 63,360 feet long.