# A triangle has sides with lengths of 8, 7, and 6. What is the radius of the triangles inscribed circle?

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To find the radius of the triangle's inscribed circle, we can use the formula:

[ r = \frac{A}{s} ]

where ( A ) is the area of the triangle and ( s ) is the semi-perimeter of the triangle.

The semi-perimeter ( s ) is calculated as:

[ s = \frac{a + b + c}{2} ]

where ( a, b, ) and ( c ) are the lengths of the triangle's sides.

The area ( A ) of the triangle can be found using Heron's formula:

[ A = \sqrt{s(s-a)(s-b)(s-c)} ]

Given the lengths of the sides of the triangle (8, 7, and 6), we can calculate the semi-perimeter ( s ) as:

[ s = \frac{8 + 7 + 6}{2} = \frac{21}{2} = 10.5 ]

Now, we can use Heron's formula to find the area ( A ):

[ A = \sqrt{10.5(10.5-8)(10.5-7)(10.5-6)} ]

[ A = \sqrt{10.5 \cdot 2.5 \cdot 3.5 \cdot 4.5} ]

[ A = \sqrt{330.75} ]

[ A \approx 18.16 ]

Finally, we can use the formula for the radius ( r ):

[ r = \frac{18.16}{10.5} ]

[ r \approx 1.73 ]

So, the radius of the triangle's inscribed circle is approximately 1.73 units.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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