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.

Explanation:

Step1: Identify similar triangles

Triangles $\triangle ABC$ and $\triangle AED$ are similar.

Step2: Define variables and ratios

Let $h$ = height of lamppost.
Base of $\triangle ABC$: $AB=2$ m, height $BC=1.8$ m.
Base of $\triangle AED$: $AE=2+1=3$ m, height $ED=h$.
Similar triangles give $\frac{BC}{ED}=\frac{AB}{AE}$

Step3: Substitute values and solve

$$\frac{1.8}{h}=\frac{2}{3}$$
Rearrange: $h=\frac{1.8\times3}{2}$

Step4: Calculate final value

$h=\frac{5.4}{2}=2.7$

Answer:

2.7