A right triangle has one leg that measures 8 units and the other leg measures 6 units. Calculate the length of the hypotenuse.

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UpStudy AI · Accepted Answer

To find the length of the hypotenuse of a right triangle when you know the lengths of the two legs, you can use the **Pythagorean Theorem**. The theorem states:

$$
\text{(Hypotenuse)}^2 = (\text{Leg}_1)^2 + (\text{Leg}_2)^2
$$

**Given:**
- Leg 1 ($$a$$) = 6 units
- Leg 2 ($$b$$) = 8 units

**Steps to Calculate the Hypotenuse ($$c$$):**

1. **Square both legs:**
   $$
   a^2 = 6^2 = 36
   $$
   $$
   b^2 = 8^2 = 64
   $$

2. **Add the squares of the legs:**
   $$
   a^2 + b^2 = 36 + 64 = 100
   $$

3. **Take the square root of the sum to find the hypotenuse:**
   $$
   c = \sqrt{100} = 10 \text{ units}
   $$

**Conclusion:**
The length of the hypotenuse is **10 units**.
The hypotenuse is 10 units long.

A right triangle has one leg that measures 8 units and the other leg measures 6 units. Calculate the length of the hypotenuse.

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