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?

Question

Marquis Crane

Mathematics

18 November, 14:32

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?

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Harold Mcneil · Answer 1

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.