Law of Sines applied problem help please

[jessilovin]

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 ? 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. Solve using law of sines.


A) Approximate the angle ?.
b) Approximate the distance d that the center of the top of the tower has moved from the perpendicular.

 

[galactus]

The angle is closer to 53.3 degrees, so that is what I'll use. OK.

Here is a start

The length AB is 179 and BC is 150.

You can use the law of sines as per the diagram to find angle at point A of the large triangle. Then you can easily find the angle it leans

\(\displaystyle \frac{150}{sin(A)}=\frac{179}{sin(53.3)}\)

Solve for A.

The, once you have that you can use 53.3+B-90=the angle you need.

Then ,the distance, d, can easily be found.

 

[jessilovin]

Ok I got theta to equal 5 degrees and I got the distance to equal 15.6 feet. Is this correct or did I make a mistake somewhere.

 

[galactus]

That is correct.