Question

a person 5 - ft tall casts a shadow 12 - ft long. at the same time, a nearby tree casts a shadow 26 - ft long. find the height of the tree.
the tree’s height is ft. (round to the nearest tenth.)

Explanation:

Step1: Set up proportion

Since the ratio of height to shadow - length is the same for the person and the tree, we can set up the proportion $\frac{h_{1}}{s_{1}}=\frac{h_{2}}{s_{2}}$, where $h_{1}$ is the height of the person, $s_{1}$ is the length of the person's shadow, $h_{2}$ is the height of the tree, and $s_{2}$ is the length of the tree's shadow. Let $h_{1} = 5$ ft, $s_{1}=12$ ft, and $s_{2}=26$ ft. Then the proportion is $\frac{5}{12}=\frac{h_{2}}{26}$.

Step2: Solve for $h_{2}$

Cross - multiply to get $12h_{2}=5\times26$. So, $12h_{2}=130$. Then $h_{2}=\frac{130}{12}=\frac{65}{6}\approx10.833\cdots$.

Step3: Round to the nearest tenth

Rounding $\frac{65}{6}\approx10.833\cdots$ to the nearest tenth gives $h_{2}\approx10.8$ ft.

Answer:

$10.8$