Observe the cone figure below. The slant height, l, is the diagonal length of the cone. The cone stands 13 feet tall and has a radius of 5, what is the length of the height of the cone?
a2 +b2 = c2
length of the height equals?
We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides. In this case, the slant height is the hypotenuse and the height is one of the other two sides.
Let's call the height of the cone "h". The slant height, "l", is given as the diagonal.
According to the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Replacing the variables with the corresponding values, we have:
h^2 + 5^2 = 13^2
Simplifying the equation, we get:
h^2 + 25 = 169
Now, let's solve for h:
h^2 = 169 - 25
h^2 = 144
Taking the square root of both sides, we get:
h = √144
Therefore, the length of the height of the cone is 12 feet.
IT WAS RIGHT YOUR THE BEST I JUST DID IT WRONG HAHA
Thank you for your kind words! I'm glad I could help clarify the solution for you. If you have any other questions, feel free to ask.
given l = 30 in w = 20 in h = 18 in, and x = 36.1 in find the length of d round the answer to the nearest tenth.
To find the length of d, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle with sides w, h, and d.
We are given:
w = 20 in
h = 18 in
x = 36.1 in
Let's find the length of d:
Using the Pythagorean theorem, we have:
d^2 = w^2 + h^2
Substituting the given values:
d^2 = (20^2) + (18^2)
d^2 = 400 + 324
d^2 = 724
Now, let's solve for d:
d = √724
Using a calculator, we find that d ≈ 26.93
Rounding to the nearest tenth, the length of d is approximately 26.9 inches.
Given l=30 in. , w=20 in. , h=18 in. , and x=36.1 in. , find the length of d . Round the answer to the nearest tenth.
(1 point)
To find the length of d, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle with sides w, h, and d.
We are given:
w = 20 in
h = 18 in
x = 36.1 in
Let's find the length of d:
Using the Pythagorean theorem, we have:
d^2 = x^2 - h^2
Substituting the given values:
d^2 = (36.1^2) - (18^2)
d^2 = 1303.21 - 324
d^2 = 979.21
Now, let's solve for d:
d = √979.21
Using a calculator, we find that d ≈ 31.3
Rounding to the nearest tenth, the length of d is approximately 31.3 inches.
wrong
Apologies for the error in my previous response. Let's try solving for the length of d again using the given values.
We are given:
l = 30 in
w = 20 in
h = 18 in
x = 36.1 in
To find the length of d, we can use the Pythagorean theorem. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
d^2 = x^2 - w^2
Substituting the given values:
d^2 = (36.1^2) - (20^2)
d^2 = 1303.21 - 400
d^2 = 903.21
Taking the square root of both sides, we get:
d ≈ √903.21
Using a calculator, we find that d ≈ 30.1.
Rounding to the nearest tenth, the length of d is approximately 30.1 inches.
To find the length of the height of the cone, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In the given cone, the slant height (l) is the hypotenuse, and the height of the cone is one of the other sides (a). The radius of the cone is equal to the length of the base, and since the base is circular, the radius (r) is the other side (b) of the right triangle.
Using the Pythagorean theorem, we can write the equation:
a^2 + b^2 = c^2
Plugging in the values from the problem:
a^2 + 5^2 = 13^2
Simplifying the equation:
a^2 + 25 = 169
Subtracting 25 from both sides:
a^2 = 169 - 25
a^2 = 144
Taking the square root of both sides:
a = √144
a = 12
Therefore, the length of the height of the cone is 12 feet.