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 $\triangle ADE$ are similar.

Step2: Set up proportion

Since similar - triangles have proportional sides, we have $\frac{BC}{DE}=\frac{AB}{AE}$. We know that $BC = 1.8$ (height of the boy), $AB = 2$ (length of the boy's shadow), and $AE=2 + 1=3$ (distance from the tip of the shadow to the lamppost). Let the height of the lamppost $DE = h$. Then $\frac{1.8}{h}=\frac{2}{3}$.

Step3: Solve for $h$

Cross - multiply to get $2h=1.8\times3$. So $2h = 5.4$, and $h=\frac{5.4}{2}=2.7$.

Answer:

$2.7$