SOLUTION: The leaning tower of Pisa was originally perpendicular to the ground and 179 feet tall. Because of sinking into the earth, it now leans at a certain angle θ from the perpendi

Algebra ->  Triangles -> SOLUTION: The leaning tower of Pisa was originally perpendicular to the ground and 179 feet tall. Because of sinking into the earth, it now leans at a certain angle θ from the perpendi      Log On


   

Question 148909: The leaning tower of Pisa was originally perpendicular to the ground and 179 feet tall. Because of sinking into the earth, it now leans at a certain angle θ from the perpendicular. When the top of the tower is viewed from a point 150 feet from the center of its base, the angle of elevation is 53 degrees.Use the Lw of Sines to solve.


A) Approximate the angle θ.
b) Approximate the distance d that the center of the top of the tower has moved from the perpendicular.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The leaning tower of Pisa was originally perpendicular to the ground and 179 feet tall. Because of sinking into the earth, it now leans at a certain angle θ from the perpendicular. When the top of the tower is viewed from a point 150 feet from the center of its base, the angle of elevation is 53 degrees.Use the Lw of Sines to solve.

A) Approximate the angle θ.
:
Let Angle A = 53 degrees, then side a = 179
Let Angle B = angle of the tower, to a point on the ground, 150' from the tower center (A)
Then b = 150
:
Find Angle B
sin%2853%29%2F179 = sin%28B%29%2F150
sin(B) = %28%28.798863%2A150%29%29%2F179
sin(B) = .6692
B = 42 degrees
:
Find 3rd angle: 180 - 53 - 42 = 85 degrees
Angle from perpendicular: 90 - 85 = 5 degrees.
:
:
b) Approximate the distance d that the center of the top of the tower has moved from the perpendicular.
:
Find the tangent of 5 degrees:
Tan(5) = d%2F179
d = .08749 * 179
d = 15.66 ft