The Leaning Tower of Pisa, leaned at an angle of approximately 84.50to the ground in 1990. The height (length) of the tower is 55.86 m. How far (how many meters) off the vertical is the top of the tower?(Answer to one decimal place and put only the numbers in the box with no units.)
Question
The Leaning Tower of Pisa, leaned at an angle of approximately 84.50to the ground in 1990. The height (length) of the tower is 55.86 m. How far (how many meters) off the vertical is the top of the tower?(Answer to one decimal place and put only the numbers in the box with no units.)
Solution
To solve this problem, we can use trigonometry. Specifically, we can use the sine function, which is defined as the ratio of the length of the side that is opposite the angle to the length of the hypotenuse in a right triangle.
Here are the steps:
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Convert the leaning angle of the tower from degrees to radians. In mathematics, angles are usually measured in radians. One degree is equal to π/180 radians. So, 84.5 degrees is equal to 84.5*(π/180) = 1.474 radians.
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The problem is asking for the horizontal distance from the base of the tower to the top of the tower, which is the opposite side in our right triangle. We can find this distance by multiplying the length of the tower (the hypotenuse) by the sine of the leaning angle.
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Calculate the distance: 55.86 * sin(1.474) = 55.1 meters.
So, the top of the tower is approximately 55.1 meters off the vertical.
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