Question

a boy who is 1.8 meters tall stands 1 meter away from a lamppos and casts a shadow 2 meters long. the height of the lamppost is meters.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle AED\), we have the proportion \(\frac{BC}{DE}=\frac{AB}{AE}\).
Let \(DE = h\) (height of lamppost). We know \(BC = 1.8\) (height of boy), \(AB=2\) (length of boy's shadow), and \(AE=2 + 1=3\) (total length from tip of shadow to base of lamppost).
Substituting into the proportion: \(\frac{1.8}{h}=\frac{2}{3}\).

Step2: Solve the proportion for \(h\)

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

Answer:

\(2.7\)