To cut down a dead tree so that it does not land on your house, you first need to find its height. You use a metal square to line up the top and bottom of the tree. The vertical distance from the ground to your eye is 6.1 feet, and the distance from you to the tree is 16 feet. Approximate the height (in feet) of the tree. Round your answer to the nearest tenth.

Calculate:

[tex] 6.1 \cdot 16 = \frac{97.6}{2} [/tex]

Choose the correct answer:

A. about 48.1 ft
B. about 97.6 ft
C. about 17.1 ft
D. about 42.0 ft

To solve the problem of finding the height of the tree, we will follow these steps:

1. Understand the Situation: You are trying to determine the height of a dead tree. You know that the vertical distance from the ground to your eye level is 6.1 feet, and you are standing 16 feet away from the tree.

2. Calculate the Height: We use the information that you've lined up the tree with a metal square from your eye level, which means you're essentially using basic trigonometry without needing angles in this specific example.

3. Multiply the Values: The height is estimated by multiplying the distance from your eye to the ground (6.1 feet) by the distance from the tree (16 feet).

[tex]\[
\text{Height of the tree} = 6.1 \times 16 = 97.6 \text{ feet}
\][/tex]

4. Round the Result: We round the computed height to the nearest tenth, which in this case remains 97.6 feet.

5. Choose the Closest Answer: From the options given:
- a. about 48.1 ft
- b. about 97.6 ft
- c. about 17.1 ft
- d. about 42.0 ft

The computed height matches option b. about 97.6 ft.

Therefore, the approximate height of the tree is about 97.6 feet.