How long does the ladder need to be?

Rapunzel is being held captive in a tower! Flynn is on the ground with a ladder. From a point on the ground 15 feet from the base of the tower, the angle of elevation to Rapunzel’s window is 60°. How long does the ladder need to be?

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A right triangle is formed.

In relation to the 60° angle:
- the 15 feet from the base of the tower is the adjacent side
- the length of the ladder is the hypotenuse {the side opposite the right angle}

adjacent
------------ = cosine
hypotenuse

x = length of the ladder

15
--- = cos 60°  {cosine of an angle = adjacent over hypotenuse}
x

x(cos 60°) = 15  {multiplied each side by x}
0.5x = 15  {cosine of 60° = 0.5}
x = 30  {divided each side by 0.5}

The ladder is 30 feet.

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