The problem states that a 17-foot tall tree casts a 10-foot shadow. Another tree casts a 35-foot shadow. We need to find the height of the second tree, rounded to the nearest tenth of a foot.

1. Problem Description

The problem states that a 17-foot tall tree casts a 10-foot shadow. Another tree casts a 35-foot shadow. We need to find the height of the second tree, rounded to the nearest tenth of a foot.

2. Solution Steps

We can set up a proportion because the ratio of the height of the tree to the length of its shadow should be the same for both trees. Let $h$ be the height of the second tree. Then we can write the proportion:

$\frac{\text{height of first tree}}{\text{length of first tree's shadow}} = \frac{\text{height of second tree}}{\text{length of second tree's shadow}}$

Substituting the given values, we get:

$\frac{17}{10} = \frac{h}{35}$

To solve for $h$, we can multiply both sides of the equation by 35:

$h = \frac{17}{10} \times 35$

$h = 1.7 \times 35$

$h = 59.5$

Therefore, the height of the second tree is 59.5 feet.

3. Final Answer

5

9. 5 feet