type the correct answer in the box. write your answer to one decimal place. a boy who is 1.8 meters tall…

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.

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.

Answer

Explanation:

Step1: Set up similar - triangles proportion

Since $\triangle ABC$ and $\triangle ADE$ are similar, the ratios of their corresponding sides are equal. Let the height of the lamppost $DE = h$. We know that $\frac{BC}{DE}=\frac{AB}{AE}$. Given $BC = 1.8$ meters, $AB = 2$ meters, and $AE=2 + 1=3$ meters. So the proportion is $\frac{1.8}{h}=\frac{2}{3}$.

Step2: Cross - multiply to solve for h

Cross - multiplying the proportion $\frac{1.8}{h}=\frac{2}{3}$ gives us $2h=1.8\times3$.

Step3: Calculate the value of h

First, calculate $1.8\times3 = 5.4$. Then, solve for $h$ from $2h = 5.4$. We get $h=\frac{5.4}{2}=2.7$.

Answer:

2.7