# A triangle has sides with lengths of 4, 9, and 8. What is the radius of the triangles inscribed circle?

Refer to the figure below

As the sides of the triangle are 4, 8 and 9:

Adding the first and last equations

Using the Law of Cosines (

In the right triangle with

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The radius ( r ) of the triangle's inscribed circle is given by the formula:

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

where ( A ) is the area of the triangle, ( a ), ( b ), and ( c ) are the lengths of its sides. The area ( A ) can be calculated using Heron's formula:

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

where ( s ) is the semiperimeter of the triangle given by:

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

Substitute the given side lengths ( a = 4 ), ( b = 9 ), and ( c = 8 ) into the formulas to find ( r ).

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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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