# An isosceles triangle has 2 sides equal to 0.96 inches and the measure of the angle between them is 104.5 degrees. What is the measure of the third side? Please show work.

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To find the measure of the third side of an isosceles triangle with two sides equal to 0.96 inches and an angle between them of 104.5 degrees, we can use the Law of Cosines. The Law of Cosines states:

[ c^2 = a^2 + b^2 - 2ab \cos(C) ]

Where:

- ( c ) is the length of the third side (which is also equal to the other two sides in an isosceles triangle).
- ( a ) and ( b ) are the lengths of the equal sides (0.96 inches in this case).
- ( C ) is the angle between the equal sides (104.5 degrees in this case).

Plugging in the values we have:

[ c^2 = (0.96)^2 + (0.96)^2 - 2(0.96)(0.96) \cos(104.5^\circ) ]

Now, calculate the cosine of 104.5 degrees:

[ \cos(104.5^\circ) \approx -0.243 ]

Plug this value back into the equation:

[ c^2 = (0.96)^2 + (0.96)^2 - 2(0.96)(0.96)(-0.243) ]

[ c^2 = 0.9216 + 0.9216 + 0.44518336 ]

[ c^2 = 2(0.9216) + 0.44518336 ]

[ c^2 = 1.8432 + 0.44518336 ]

[ c^2 = 2.28838336 ]

Now, take the square root of both sides to find ( c ), the length of the third side:

[ c = \sqrt{2.28838336} ]

[ c \approx 1.51 , \text{inches} ]

So, the measure of the third side of the isosceles triangle is approximately 1.51 inches.

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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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