The problem states that a right triangle has a hypotenuse of 8 cm and one leg of 4 cm. We need to find the length of the other leg, rounded to the nearest tenth.

1. Problem Description

The problem states that a right triangle has a hypotenuse of 8 cm and one leg of 4 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 for a right triangle with legs $a$ and $b$, and hypotenuse $c$, the following relationship holds:

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

In this problem, we are given $c = 8$ cm and $a = 4$ cm. We need to find $b$.

Substituting the given values into the Pythagorean theorem:

$4^2 + b^2 = 8^2$

$16 + b^2 = 64$

$b^2 = 64 - 16$

$b^2 = 48$

$b = \sqrt{48}$

To simplify $\sqrt{48}$, we can find the prime factorization of 48: $48 = 16 \times 3 = 2^4 \times 3$. Therefore, $\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$.

Now, we need to approximate the value of $4\sqrt{3}$ to the nearest tenth.

Since $\sqrt{3} \approx 1.732$, we have:

$b = 4\sqrt{3} \approx 4 \times 1.732 = 6.928$

Rounding to the nearest tenth, we get $b \approx 6.9$.

3. Final Answer

6. 9