# Math

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The leaning tower of Pisa is 55.9 m tall and leans 5.5 degrees from the vertical. If its shadow is 90 m long, what is the distance from the top of the tower to the top of the edge of its shadow, assuming the ground around the tower is level?

• Math -

the tower makes an angle of 84.5º with the ground.
let x m be the length of the shadow, then by the Cosine Law

x^2 = 90^2 + 55.9^2 - 2(90)(55.9)cos 84.5º
etc.

• Math -

where did you get the 84.5º from?

• Math -

thanks so much!

• Math -

oh yeah that's true where does the 84.5 degrees come from?

• Math -

A vertical makes a right-angle with the horizontal
The tower is off 5.5º from the vertical.

5.5º + ? = 90 ??

• Math -

84.5 degrees:
90+5.5=95.5
180-95.5=84.5

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