Consult the figure To find the length of the span of a propo

Consult the figure. To find the length of the span of a proposed ski lift from P to Q, a surveyor measures the angle of DPQ to be 25 degrees and then walks back a distance of 1000 feet to R and measures angle PRQ to be 15 degrees. What is the distance from P to Q? Find the height of the mountain.

Solution

Triangle PQR : AngleRPQ = 180 -25 = 155deg

Angel PQR = 180 -155 - 15 = 180 - 170 = 10 deg

applying sine rule: PQ/sin15 = 1000/sin10

PQ = 1490.48 feet

Height of mountain DQ : DQ/PQ = sin25

DQ = 1490.48*sin25 = 699.73 feet