Frank stands 500 feet from the base of the statue of liberty. if frank looks up with an angle of elevation of 30', how tall is the statue of liberty, to the nearest foot?

289 ft.

Explanation:

You can form a right triangle with these features:

1) Base = adjacent-leg = 500 feet

2) angle between the hypotenuse and the base = 30° ( I use 30° instead of 30', because 30' does not make sense, it is a too small angle)

3) Height = opposite-leg = height of the Statue of LIberty = x

Now, use the equation for the trigonometric ratio tangent:

tan(angle) = opposite-leg / adjacent-leg

=> tan (30°) = x / 500ft

=> x = 500ft * tan(30°)

x = 288.67 ft which rounded to the nearest foot is 289 ft.