Law of Sines Word Problem (Photo Included)

[TrueStar]

Homework Statement

The leaning tower of Pisa was originally perpendicular to the ground and 179ft tall. Because of sinking into the earth, it now leans at a certain angle 'theta' from the perpendicular, as shown in the figure. When the top of the tower is viewed from a point 150ft from the center of its base, the angle of elevation is 53 degrees.

a) Approximate the angle theta.

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

Here is the photo. I apologize for the blurry photo. If needed I'll try to get my real camera and take a better one.

Homework Equations

Law of Sines. Maybe one can solve this by other means, but it is implied I can do this with Law of Sines alone.

The Attempt at a Solution

I know the height of the tower is the the length of one side of the right triangle (the straight line on the tower in the photo). I'm not sure if that is also true for the line the represents how the tower leans. I'm not sure where to start with this as a result. I think I need a nudge in the right direction.

Thanks!

 

[srmeier]

you know that:

$$\frac{sin(53)}{H_a}$$ - with $$H_a$$ being the height after

is equal to what?

 

[TrueStar]

That would equal to sin c\150 feet. That is, if sin c is the angle at the top for the triangle involving H_a.

Am I supposed to know how to get that angle..or am I really off track?

 

[willem2]

That would equal to sin c\150 feet. That is, if sin c is the angle at the top for the triangle involving H_a.

Am I supposed to know how to get that angle.

yes.

 

[TrueStar]

OK, I slept on it and worked on it a bit more this morning. I think the angle that is opposite to the ground is 37 degrees. Therefore:

sin 53\H_a=sin 37\150

I found this angle by finding all angles of the right triangle and then creating two more right triangles between the perpendicular and H_a.

 

[zeion]

But 37 is no longer the third angle after the tower has leaned no?

 

[TrueStar]

I thought that was odd. I just don't know how to find this angle. After leaning, should it be larger than 37 degrees?

 

[TrueStar]

OK I think I have a correct answer. The angle theta is 5 degrees and the distance d is about 15.7 feet. I let the length of the perpendicular and the leaning part be equal to 179 feet. I don't know if that's what the diagram implied though.