The sides of a triangle measure 6 inches, 8 inches, and 10 inches. The triangle has one $$ 90^{\circ} $$ angle. What type of triangle is it?

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To determine the type of triangle based on the given side lengths, we can use the properties of triangles, particularly the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Given the sides of the triangle:
- $$ a = 6 $$ inches
- $$ b = 8 $$ inches
- $$ c = 10 $$ inches (the longest side)

We can check if this triangle is a right triangle by verifying the Pythagorean theorem:

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

Now, let's calculate $$ c^2 $$ and $$ a^2 + b^2 $$:

1. Calculate $$ c^2 $$:
   $$
   c^2 = 10^2 = 100
   $$

2. Calculate $$ a^2 + b^2 $$:
   $$
   a^2 + b^2 = 6^2 + 8^2 = 36 + 64 = 100
   $$

Now we can compare the two results:

$$
c^2 = 100 \quad \text{and} \quad a^2 + b^2 = 100
$$

Since $$ c^2 = a^2 + b^2 $$, this confirms that the triangle is a right triangle.

Thus, the type of triangle is a **right triangle**.
The triangle is a right triangle.

The sides of a triangle measure 6 inches, 8 inches, and 10 inches. The triangle has one \( 90^{\circ} \) angle. What type of triangle is it?

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