Question

the original height of the leaning tower of pisa was 184 1/2 feet. at a distance of 140 feet from the base of the tower, the angle of elevation from the ground to the top of the tower is 59°. how far is the tower leaning from the original vertical position?

Answer 1

b on edge

Explanation:

Answer 2

Tower is leaning by 9.6° from it's vertical position.

Explanation:

From the figure attached AB represents the leaning tower with the original height 184.5 feet.

From a point C which is 140 feet apart angle of elevation of the top of the tower is 59°.

We have to find the angle x by which tower AB is leaning from the original vertical position.

By sine rule in triangle ABC.

`(sin59)/(184.5)=(sinA)/(140)`

`sinA=((sin59)(140))/(184.5)`

sinA =
`((0.8571)(140))/((184.5))`

A =
`sin^(-1)(0.6504)`

A = 40.57°

Since ∠A + ∠B + ∠C = 180°

40.57 + ∠B + 59 = 180

99.57 + ∠B = 180

∠B = 180 - 99.57

∠B = 80.43°

Now we have to calculate the measure of ∠x .

Since ∠x = 90° - ∠B

∠x = 90 - 80.43

= 9.57°≈ 9.6°

Therefore, Tower is leaning by 9.6° from it's vertical position.