Katie is watching a helicopter flying at an altitude of 5 miles. if the angle of elevation is pi/3 , the distance between katie and the helicopter is approximately miles.

From SOH CAH TOA, you know that
.. Sin = Opposite/Hypotenuse
.. sin(π/3) = (5 miles)/Hypotenuse
.. Hypotenuse = (5 miles)/sin(π/3) = 5/(√3/2) miles ≈ 5.774 miles

The straight-line distance from Katie to the helicopter is about 5.77 miles.