We are given a right triangle with a hypotenuse of 8 cm and one leg of 6 cm. We need to find the length of the other leg, rounded to the nearest tenth.

1. Problem Description

We are given a right triangle with a hypotenuse of 8 cm and one leg of 6 cm. We need to find the length of the other leg, rounded to the nearest tenth.

2. Solution Steps

We can use the Pythagorean theorem to solve for the missing leg. The Pythagorean theorem states that in a right 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 (legs). The formula is:

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

where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse.

In this problem, we are given $c = 8$ cm and one leg, let's say $a = 6$ cm. We want to find $b$.

Plugging the values into the formula, we get:

$6^2 + b^2 = 8^2$

$36 + b^2 = 64$

Subtract 36 from both sides:

$b^2 = 64 - 36$

$b^2 = 28$

Take the square root of both sides:

$b = \sqrt{28}$

$b \approx 5.2915$

Round to the nearest tenth:

$b \approx 5.3$

3. Final Answer

The length of the other leg is approximately 5.3 cm.