Question

1. on a sunny day josée’s shadow is 2.9 m long, while the shadow of a tower is 11.3 m long. if josée is 1.8 m tall, calculate the height of the tower.

Explanation:

Step1: Set up proportion (similar triangles)

Since the triangles are similar, the ratios of corresponding sides are equal. So, $\frac{\text{José's height}}{\text{José's shadow length}} = \frac{\text{Tower's height}}{\text{Tower's shadow length}}$. Let $h$ be the tower's height. Then $\frac{1.8}{2.9} = \frac{h}{11.3}$.

Step2: Solve for \( h \)

Cross - multiply: $2.9h = 1.8\times11.3$. First, calculate $1.8\times11.3 = 20.34$. Then, $h=\frac{20.34}{2.9}$.

Step3: Calculate the division

$\frac{20.34}{2.9}=7.01379\cdots\approx7.0$ (rounded to a reasonable decimal place)

Answer:

The height of the tower is approximately $\boldsymbol{7.0}$ meters (or more precisely, about $7.01$ meters).