Question

A sightseer near the top of the Empire State Building, 950 feet above the ground, looks down at a 5° angle of depression to an intersection near Central Park. How far away is the intersection from the base of the Empire State Building?
Select one:
a. 2.05 miles
b. 1.01 miles
c. 0.63 miles
d. 0.18 miles

Answer 1

Check the picture below.

make sure your calculator is in Degree mode.

now, "x" is just how many feet it is away, how many miles is that?

well, we know that there are 5280 feet in 1 mile, so

$\bf x=\stackrel{in~feet}{\cfrac{950}{tan(5^o)}}\qquad \qquad\qquad \qquad \qquad x=\stackrel{in~miles}{\cfrac{\quad \frac{950}{tan(5^o)}\quad }{5280}}$