We need to calculate the length of a zip line connecting the tops of two buildings. One building is 130 ft tall, and the other is 30 ft tall. The horizontal distance between the buildings is 72 ft. We need to round the answer to the nearest tenth.

1. Problem Description

We need to calculate the length of a zip line connecting the tops of two buildings. One building is 130 ft tall, and the other is 30 ft tall. The horizontal distance between the buildings is 72 ft. We need to round the answer to the nearest tenth.

2. Solution Steps

The height difference between the buildings is $130 - 30 = 100$ ft. This forms one leg of a right triangle.

The horizontal distance between the buildings, 72 ft, forms the other leg of the right triangle.

The length of the zip line is the hypotenuse of this right triangle.

We use the Pythagorean theorem to find the length of the hypotenuse, $c$.

$a^2 + b^2 = c^2$

where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse.

In our case, $a = 100$ and $b = 72$.

$c = \sqrt{a^2 + b^2}$

$c = \sqrt{100^2 + 72^2}$

$c = \sqrt{10000 + 5184}$

$c = \sqrt{15184}$

$c \approx 123.2233$

We need to round the result to the nearest tenth.

$c \approx 123.2$ ft

3. Final Answer

123.2 ft