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grin007 [14]
2 years ago
15

1. A length of rope is stretched between the top edge of a building and a stake in the ground. The head of the stake is at groun

d level. The rope also touches a tree that is growing halfway between the stake and the building. If the tree is 38 feet tall, how tall is the building? stake A.38 ft B. 19 ft C.76 ft. D.57 ft.​
Mathematics
1 answer:
denpristay [2]2 years ago
4 0

Answer:

19

Step-by-step explanation:

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Step2247 [10]

Answer:

A = 297\pi

Step-by-step explanation:

To solve this problem we need to be familiar with the formula for the surface area of a cone:

A = \pi r(r + \sqrt{h^2+r^2})

We are given the length of a side and the diameter, to calculate the radius divide the diameter in half:

r = \frac{d}{2}\\r = \frac{18}{2}\\r = 9 cm

To calculate the height of the cone, we must use the Pythagorean Theorem:

C^2 = A^2 + B^2

We can treat the side length as the hypotenuse C, the radius as the base A, and solve for height B. Set the expression up like this:

C^2 = A^2 + B^2\\24^2 = 9^2 + B^2\\B^2 = 24^2 - 9^2\\B = \sqrt{24^2 - 9^2}\\B = \sqrt{576 - 81}\\B = \sqrt{495}\\B \approx 22.25

Now we can plug into our original formula:

A = \pi r(r + \sqrt{h^2+r^2})\\A = \pi 9(9+\sqrt{\sqrt{495}^2+9^2}\\A = \pi 9(9+\sqrt{495 + 81}\\A = \pi 9(9+\sqrt{576})\\A = \pi 9(9 + 24)\\A = \pi 9(33)\\A = 297\pi

5 0
2 years ago
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