The problem asks us to find the length of the cable $GF$ given that the length of the sign $FH$ is 3 meters and the distance $GH$ is 1.4 meters. We need to use the Pythagorean theorem to solve this problem and give the answer to 1 decimal place.

1. Problem Description

The problem asks us to find the length of the cable $GF$ given that the length of the sign $FH$ is 3 meters and the distance $GH$ is 1.4 meters. We need to use the Pythagorean theorem to solve this problem and give the answer to 1 decimal place.

2. Solution Steps

The Pythagorean theorem states that in a right-angled 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.

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

In this case, $GF$ is the hypotenuse of the right-angled triangle $GFH$. $FH$ is the length of the sign, which is 3 meters, and $GH$ is the distance from the base of the sign to the point where the cable is secured, which is 1.4 meters.

We can use the Pythagorean theorem to find the length of $GF$.

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

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

$GF^2 = 9 + 1.96$

$GF^2 = 10.96$

$GF = \sqrt{10.96}$

$GF \approx 3.310589$

We need to round the answer to 1 decimal place.

$GF \approx 3.3$

3. Final Answer

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