A fish shop has a vertical sign of height $|FH| = 3$ m. A cable is tied from the top of the sign, $F$, to a point $G$ on the ground, which is $1.4$ m from the base of the sign, $H$. We need to find the length of the cable, $|GF|$, using the Pythagorean theorem and round the answer to 1 decimal place.

1. Problem Description

A fish shop has a vertical sign of height $|FH| = 3$ m. A cable is tied from the top of the sign, $F$, to a point $G$ on the ground, which is $1.4$ m from the base of the sign, $H$. We need to find the length of the cable, $|GF|$, using the Pythagorean theorem and round the answer to 1 decimal place.

2. Solution Steps

Since the sign is vertical, we have a right-angled triangle $\triangle FHG$ with a right angle at $H$. We are given that $|FH| = 3$ m and $|GH| = 1.4$ m. We need to find $|GF|$.

By the Pythagorean theorem, we have

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

Substituting the given values, we have

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

$|GF|^2 = 9 + 1.96$

$|GF|^2 = 10.96$

Taking the square root of both sides, we get

$|GF| = \sqrt{10.96}$

$|GF| \approx 3.310589$

Rounding to 1 decimal place, we get

$|GF| \approx 3.3$ m

3. Final Answer

3.3 m