The stadium light poles for a soccer field are located 24 feet from the sideline

Question

The stadium light poles for a soccer field are located 24 feet from the sideline. The lamp at the top of each 54 foot pole needs to be set at an angle upward from the pole so that the center of the light beam hits the soccer field 31 feet inside the sideline toward the center of the field. Begin by drawing a diagram of the situation and label each known and unknown quantity.

a. At what angle (measured in degrees) should the lamp be set to meet the stated conditions?

b. Based on the angle you found in part (a), if the measure of that angle increases by 1 degree, what is the increase in the distance from the base of the pole to where the center of the light hits the field?

Explanation / Answer

tan(theta) = (24+31)/54
theta = 45.52 deg

new angle = 46.52 deg
increase in distance = 54*tan(46.52) - 55 = 1.943 feet

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