A right triangle has a hypotenuse measuring 10 units and one of the legs measuring 6 units. Determine the length of the missing leg using the Pythagorean theorem.

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To determine the length of the missing leg in a right triangle using the Pythagorean theorem, follow these steps:

### **Pythagorean Theorem Overview**
The Pythagorean theorem states that in a right-angled triangle:

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

Where:
- **Legs** are the two sides that form the right angle.
- **Hypotenuse** is the side opposite the right angle and is the longest side of the triangle.

### **Given:**
- Hypotenuse ($$ c $$) = 10 units
- One leg ($$ a $$) = 6 units

### **Find:**
- The length of the missing leg ($$ b $$)

### **Application of the Theorem:**
Plug the known values into the Pythagorean theorem equation:

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

$$
6^2 + b^2 = 10^2
$$

$$
36 + b^2 = 100
$$

### **Solve for $$ b^2 $$:**

$$
b^2 = 100 - 36
$$

$$
b^2 = 64
$$

### **Find $$ b $$:**

$$
b = \sqrt{64}
$$

$$
b = 8 \text{ units}
$$

### **Conclusion:**
The length of the missing leg is **8 units**.
The missing leg is 8 units long.

A right triangle has a hypotenuse measuring 10 units and one of the legs measuring 6 units. Determine the length of the missing leg using the Pythagorean theorem.

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