The problem asks us to find the length of the missing leg of a right triangle. The hypotenuse has length 7.7 km, and one leg has length 1.9 km. We need to find the length of the other leg, denoted by $b$, and round the answer to the nearest tenth.

1. Problem Description

The problem asks us to find the length of the missing leg of a right triangle. The hypotenuse has length 7.7 km, and one leg has length 1.9 km. We need to find the length of the other leg, denoted by $b$, and round the answer to the nearest tenth.

2. Solution Steps

We can use the Pythagorean theorem to solve for the missing leg length. The Pythagorean theorem states that for a right triangle with legs of length $a$ and $b$, and hypotenuse of length $c$, we have $a^2 + b^2 = c^2$.

In this case, we are given $c = 7.7$ km and $a = 1.9$ km. We want to find $b$. Plugging in the given values, we have:

$$

1. 9^2 + b^2 = 7.7^2$

$$

2. 61 + b^2 = 59.29$

$b^2 = 59.29 - 3.61$

$b^2 = 55.68$

Now we take the square root of both sides to solve for $b$:

$b = \sqrt{55.68} \approx 7.46189$

We are asked to round to the nearest tenth, so we have $b \approx 7.5$ km.

3. Final Answer

7. 5