A street light is mounted on a pole. The tip of the shadow of a man who is standing on a street a short distance from the pole has an angle of elevation to the top of his head of 28°. A woman standing in the opposite direction of the pole as the man was standing on the same street has a angle of elevation from the tip of her shadow to her head of 24°. If the two people are 20 feet apart, how far is the street light from the head of the woman?
suppose h=height of street light x=distance of woman from pole, 20-x=distance of man from pole tan 24=x/h=0.445 tan 28=(20-x)/h=0.532 re-arranging the above we get: x=0.445h 20-x=0.532h thus the value of h will be given by: 20=0.977h hence h=20.5 ft
substituting the values we get: x=woman's position =9.1 ft from the pole and the man is 10.9 ft away.
