SOLUTION: In 2000, 70 tonnes of soil were removed from under the Leaning Tower of Pisa, and the angle the tower made with the ground was increased by about 0.5 degrees.Before that a point ne

Question 126728: In 2000, 70 tonnes of soil were removed from under the Leaning Tower of Pisa, and the angle the tower made with the ground was increased by about 0.5 degrees.Before that a point near the top of the tower was 50.5m from a point at the base (measured along the tower), and this top point was directly above a point on the ground 4.25m from the same base point. How much did the point on the ground move toward the base point?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the angle the tower made with the ground was increased by about 0.5 degrees.Before that a point near the top of the tower was 50.5m from a point at the base (measured along the tower), and this top point was directly above a point on the ground 4.25m from the same base point. How much did the point on the ground move toward the base point?
:
I picture this as a right triangle; the hypotenuse is the tower, given as 50.5 m forms an angle with the ground. (Call it "A") The base is 4.25 m to the right angle
:
Use the cosine to find the angle (A) before the tower was shifted.
Side adjacent = 4.25, Hypotenuse = 50.5
Cos(A) =
A = 85.172 degrees
:
If .5 degrees is added to it: 85.172 + .5 = 85.672 degrees is angle A now
:
Find the new side adjacent, call it x:
Cos(85.672) =
.075466 =
x = .075466 * 50.5
x = 3.81 m is the side after shifting of the tower .5 degree
:
Find the distance the point moved: 4.25 - 3.81 = .44 meter or 44 cm
:
Did I make this clear? Any questions?

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