Answer:
Tower is leaning by 9.6° from it's vertical position.
Step-by-step 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.
\(\frac{sin59}{184.5}=\frac{sinA}{140}\)
\(sinA=\frac{(sin59)(140)}{184.5}\)
sinA = \(\frac{(0.8571)(140)}{(184.5)}\)
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.
