As shown in the figure below a cable car carries passengers

As shown in the figure below, a cable car carries passengers from a point A, which is 1.2 miles from a point B at the base of a mountain, to a point P at the trip of the mountain. The angles of elevation of P from A and B are a = 21 degree and beta = 70 degree, respectively. (Round your answers to one decimal place.) Approximate the distance between A and P. Approximate the height of the mountain

Solution

Alpha = 21 deg

Beta = 70 deg

Angle B = 180 – 70 = 110 deg

Then Angle P = 180 – 21 – 110 = 49 deg

Now   sin49/1.2 = sin110/AP ========> AP = 149 miles