The Leaning Tower of Pisa in Italy leans because it was buil

The Leaning Tower of Pisa in Italy leans because it was built on unstable soil—a mixture of clay, sand, and water. The tower is approximately 58.36 meters tall from its foundation (see figure). The top of the tower leans about 5.45 meters off center.

(a) Find the angle of lean of the tower. (Round your answer to two decimal places.)
°

(b) Write as a function of d and , where is the angle of elevation to the sun.
=   

(c) Use the Law of Sines to write an equation for the length d of the shadow cast by the tower in terms of .
d =   

(d) Use a graphing utility to complete the table. (Round your answers to two decimal places.)

Solution

a) tan(alpha) = 5.45/58.36

= 5.335 deg

b) apply sine rule:

d/sin(beta) = 58.36/sin(theta)

sin(beta) = d*sin(theta)/58.36

beta = sin^-1[d*sin(theta)/58.36]

c) sin(beta) = d*sin(theta)/58.36

beta = 180 - (90+theta+ alpha) = 90 - theta- alpha

sin(beta) = sin(90 - theta- alpha) = cos(theta +alpha)

So, d = sin(beta)*58.36/sintheta

= cos(theta+ alpha)*58.36/sin(theta)

d) theta = 10 deg

Plug : theta = 10 deg, alpha = 5.33 deg and solve for d

d = cos(5.33+ 10)*58.36/sin10 = 324.12 mt