Answer:
About 76.5 ft.
Explanation:
Draw a diagram of a right triangle. The shorter leg represents the height of the main entrance of the library, which is 8 ft. The longer leg won't matter in this case. The hypotenuse is what we're trying to find, so mark it as x. We know there's a 6° angle of elevation, so the 30° angle of the triangle will be 6° in this case. Now we have to use trig. Think of Soh Cah Toa. The 6° is opposite from 8 and the hypotenuse is x. So, the equation to find x would be:
sin (6°) = 8/x
Multiply both sides by x
sin (6°) * x = 8
Divide both sides by sin (6°)
x = 8/sin (6°)
When putting it into a calculator, your answer should be 76.534, which rounds to 76.5 ft.