An airplane flying at an altitude of 6 miles is on a flight

An airplane, flying at an altitude of 6 miles, is on a flight path that goes directly over you If theta is the angle of elevation, find the distance from the observer to the plane. Note, the picture below is not to scale. Find the distance from the person to the plane if theta = 30 (without a calculator, ).

Solution

Let the distance from observer to the plane is xmiles

Sin theta=6/x

Sin 30=6/x

x=6/sin 30

x=12 miles