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julia is standing 2 feet away away from a lamppost. she casts a shadow of 5 feet and the light make a 20 degree angle relative to the ground from the top of her shadow. Does the expression give you the height of the lamppost

Respuesta :

Height of the lamp post is 2.5 ft.

Step-by-step explanation:

AB = lamp post

CD = Julia

CE = Shadow

AC = 2 ft , CE = 5 ft , ∠AEB = 20°

AE = AC+ CE = 2+ 5 = 7 ft

Considering ABE as a right triangle, we can write the tan ratio as,

tan ∠AEB = opp/adj = AB/AE

AB = AE × tan ∠AEB

    = 7 × tan 20°

  = 2.5 ft

So, height of the lamp post is 2.5 ft.

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