We are given a right triangle $GFH$ where $FH = 3$ m and $GH = 1.4$ m. We need to find the length of the hypotenuse $GF$ using the Pythagorean theorem and round the answer to one decimal place.

1. Problem Description

We are given a right triangle $GFH$ where $FH = 3$ m and $GH = 1.4$ m. We need to find the length of the hypotenuse $GF$ using the Pythagorean theorem and round the answer to one decimal place.

2. Solution Steps

We are given that the triangle $GFH$ is a right triangle. We can use the Pythagorean theorem to find the length of the hypotenuse $GF$.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In our case, $GF$ is the hypotenuse, and $FH$ and $GH$ are the other two sides. So, we have:

$GF^2 = FH^2 + GH^2$

We are given $FH = 3$ m and $GH = 1.4$ m. Substituting these values into the equation, we get:

$GF^2 = 3^2 + 1.4^2$

$GF^2 = 9 + 1.96$

$GF^2 = 10.96$

To find $GF$, we take the square root of both sides:

$GF = \sqrt{10.96}$

$GF \approx 3.31058904$

We need to round the answer to one decimal place. Since the second decimal place is 1, we round down.

$GF \approx 3.3$

3. Final Answer

The length of the cable $|GF|$ is approximately 3.3 m.