Question

Frank stands 500 feet from the base of the Statue of Liberty. If Frank looks up with an angle of elevation of 31', how tall is the Statue of Liberty, to the nearest foot?

Answer 1

In angles 31' means 31 minutes. And one degree is equal to 60 minutes, then 31' is 31/60 ° = 0.51667 °

That measure is too small if you use it you will obtain this result:

x = 500 ft * tan (31/60°) = 4.51 ft which is too little.

I will answer the problem using 31° instead of 31'.

This is answer and full explanation:

Answer: 300 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 = 31°

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 (31°) = x / 500ft

=> x = 500ft * tan(31°)

x = 300.43 ft which rounded to the nearest foot is 300 ft.