The Leaning Tower of Pisa and the Cosine Law
The Leaning Tower of Pisa is $55.9$m tall and leans $5.5^{\circ}$ from the vertical. I its shadow is $90.0$m long, what is the distance from the top of the tower to the top edge of its shadow? Assume that the ground around the tower is level. Round your answer to the nearest metre.
I drew a diagram to help me understand better,
Now using the Cosine Law,
$$c^2 = a^2 +b^2 -2ab \cos(c) \\ c^2 = (55.9)^2+(90)^2-2(55.9)(90)\cos(5.5) \\ c = \sqrt {(55.9)^2+(90)^2-2(55.9)(90)\cos(5.5)} \\ c = 34.7725 \\ c= 35$$
Apparently this is a wrong answer. The correct answer is $101$m.
What have I done wrong?
Thank you
$\endgroup$ 31 Answer
$\begingroup$The leaning angle of the tower is $5.5^\circ$. This is the angle between the tower and an upright line. As the problem reads:
and leans $5.5^\circ$ from the vertical
That means that the angle between the tower and the floor is $90-5.5=84.5^\circ$.
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