posted by George on .
A 5 foot tall woman stands 15 ft from a statue. She must look up at an angle of 60° to see the top of the statue. How tall is the statue?
It's easier if you drew the figure, but it's hard to draw figures here so I'll just describe it. :3
Note that the woman is 15 ft from the statue, and she looks up at an angle of 60° in order to see the top of statue. From here we can actually form a right triangle, with base 15 ft, the height unknown, and 60° angle between the hypotenuse and base.
Let h = height of triangle, which is also the height of statue minus the height of woman. Thus,
tan 60° = h / 15
h = 15 * tan 60°
h = 15*sqrt(3)
Therefore the total height of statue is h plus the height of woman, which is 15*sqrt(3) + 5 ft, or 30.98 ft
Hope this helps~ :3