We are given a right triangle FHG, where FH represents the height of a sign and HG represents the horizontal distance from the base of the sign to where a cable is secured. We are given that $FH = 3$ m and $HG = 1.4$ m. We need to find the length of the cable GF using the Pythagorean theorem, correct to one decimal place.

1. Problem Description

We are given a right triangle FHG, where FH represents the height of a sign and HG represents the horizontal distance from the base of the sign to where a cable is secured. We are given that $FH = 3$ m and $HG = 1.4$ m. We need to find the length of the cable GF using the Pythagorean theorem, correct to one decimal place.

2. Solution Steps

We are given a right triangle FHG, where $\angle FHG = 90^\circ$. We are given the lengths of the two sides FH and HG, and we want to find the length of the hypotenuse GF.

Using the Pythagorean theorem, we have:

$GF^2 = FH^2 + HG^2$

Substituting the given values:

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

$GF^2 = 9 + 1.96$

$GF^2 = 10.96$

Taking the square root of both sides:

$GF = \sqrt{10.96}$

$GF \approx 3.31058907 \ldots$

Rounding to one decimal place, we get:

$GF \approx 3.3$ m

3. Final Answer

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