Astreet 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 30°. 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 41°. if the two people are 40 feet apart, how far is the street light from the head of the woman?

  21.15 ft

Step-by-step explanation:

The angle at the lamp between the two shadow tips is ...

  180° -30° -41° = 109°

This angle is opposite the 40-ft side of the triangle. The distance (d) in question is opposite the 30° angle, so can be found from the Law of Sines as ...

  d/sin(30°) = 40'/sin(109°)

  d = (40')·sin(30°)/sin(109°) ≈ 21.152'

The distance from the light to the woman's head is about 21.15 feet.

_____

We have to assume the heads are at the same height.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

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