We are given a right triangle with hypotenuse 8.3 mm and one leg 3.1 mm. We need to find the length of the other leg, denoted by $a$, and round the result to the nearest tenth.

1. Problem Description

We are given a right triangle with hypotenuse 8.3 mm and one leg 3.1 mm. We need to find the length of the other leg, denoted by $a$, and round the result to the nearest tenth.

2. Solution Steps

We will use the Pythagorean theorem, which states that for a right triangle with legs $a$ and $b$ and hypotenuse $c$, $a^2 + b^2 = c^2$.

In this case, we have $a^2 + (3.1)^2 = (8.3)^2$.

We want to find $a$, so we can rearrange the equation as follows:

$a^2 = (8.3)^2 - (3.1)^2$.

Calculate the squares:

$8.3^2 = 68.89$

$3.1^2 = 9.61$

Substitute the values into the equation:

$a^2 = 68.89 - 9.61$

$a^2 = 59.28$

Now, take the square root of both sides:

$a = \sqrt{59.28}$

$a \approx 7.69935$

We are asked to round to the nearest tenth, so we look at the hundredths place, which is

9. Since 9 is greater than or equal to 5, we round up the tenths place.

$a \approx 7.7$

3. Final Answer

7.7