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The light from a lamp casts a shadow of a man standing 10 feet away from the lamppost. The shadow is 7 feet long. The angle of elevation from the tip of the shadow to the lamp is 50. To the nearest foot, the lamppost is _____ feet tall.

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haybug275
20.26 ft is the height of the lamppost

Answer:

Lamppost is 20.26 ft. tall.

Step-by-step explanation:

In the figure attached. AB is the lamp post and DE is a man standing 10 ft away from the lamp post.

Therefore, in ΔABC,

term 50° = [tex]\frac{AB}{BC}[/tex]

term 50° = [tex]\frac{AB}{17}[/tex]

1.192 = [tex]\frac{AB}{17}[/tex]

AB = 17 × 1.192

= 20.26 ft.

Therefore, Lamppost is 20.26 ft. tall.

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