Question

A man wants to zipline from the top of a 20 meter building to an island 50 meters away. How long does the zipline wire need to be? Answer to the nearest tenth.

Answer 1

To determine the length of the zipline wire, we can use the Pythagorean theorem. The situation can be visualized as a right triangle where:

- One leg (height of the building) is 20 meters,
- The other leg (horizontal distance to the island) is 50 meters,
- The hypotenuse (length of the zipline) is what we need to find.

According to the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

where \( c \) is the hypotenuse, and \( a \) and \( b \) are the two legs of the triangle.

Here, we have:
- \( a = 20 \) meters (height of the building),
- \( b = 50 \) meters (horizontal distance).

Substituting the values into the formula:

\[
c^2 = 20^2 + 50^2
\]
\[
c^2 = 400 + 2500
\]
\[
c^2 = 2900
\]

To find \( c \), we take the square root of 2900:

\[
c = \sqrt{2900}
\]

Calculating that:

\[
c \approx 53.8516
\]

Rounding to the nearest tenth, the length of the zipline wire needs to be approximately **53.9 meters**.