Question

type the correct answer in the box. write your answer to one decimal place.
a boy who is 1.8 meters tall stands 1 meter away from a lamppost and casts a shadow 2 meters long.
the height of the lamppost is
meters.
image of a triangle with points a, b, e, d, c; labeled shadow, boy, lamppost
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Explanation:

Step1: Identify similar triangles

The triangles formed by the boy and his shadow, and the lamppost and its shadow are similar. Let the height of the lamppost be \( h \) meters. The base of the boy's triangle is \( 2 \) meters (shadow), and the base of the lamppost's triangle is \( 2 + 1=3 \) meters (shadow + distance from boy to lamppost). The height of the boy is \( 1.8 \) meters.

Step2: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. So, \(\frac{1.8}{2}=\frac{h}{3}\)

Step3: Solve for \( h \)

Cross - multiply: \( 2h = 1.8\times3 \)
\( 2h=5.4 \)
Divide both sides by 2: \( h=\frac{5.4}{2}=2.7 \)

Answer:

2.7