If a triangle has sides of length 8cm, 8cm, and 5cm, how do I find the measure of the angle between the two equal sides?

Answer 1

Use the cosine rule to find the angle as #36,42^@#.

The cosine rule states that for a triangle of sides #a, b, and c#, and with angle #theta# opposite side #a#, the following relationship holds :
#a^2=b^2+c^2-2bc cos theta#.

Applying this rule to the given problem yields :

#5^2=8^2+8^2-2*8*8*cos theta#
#therefore theta= cos^(-1)((25-2*64)/(-128))=36,42^@#.
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Answer 2

You can use the Law of Cosines to find the measure of the angle between the two equal sides of the triangle. The Law of Cosines states that for any triangle with sides of lengths ( a ), ( b ), and ( c ), and the angle opposite side ( c ) is ( C ), the following equation holds:

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

Given that the triangle has sides of length 8 cm, 8 cm, and 5 cm, you can substitute these values into the equation:

[ 5^2 = 8^2 + 8^2 - 2(8)(8) \cos(C) ]

Solve for ( \cos(C) ) by rearranging the equation:

[ 25 = 64 + 64 - 128 \cos(C) ] [ 25 = 128 - 128 \cos(C) ] [ 128 \cos(C) = 128 - 25 ] [ 128 \cos(C) = 103 ]

Divide both sides by 128:

[ \cos(C) = \frac{103}{128} ]

Now, use the inverse cosine function to find the measure of angle ( C ):

[ C = \cos^{-1} \left( \frac{103}{128} \right) ]

Calculate the value of ( C ) using a calculator, and you will get the measure of the angle between the two equal sides of the triangle.

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Answer from HIX Tutor

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.

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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