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.