How do you solve a triangle if you are given A = 120 degrees, b = 3, c = 10?
Applying the Law of Cosines,
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To solve a triangle when given one angle and two sides, you can use the Law of Sines and Law of Cosines. Here's how to proceed:
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First, use the Law of Sines to find the ratio of the lengths of the sides to the sines of their opposite angles. This law states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} ]
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Given angle ( A = 120^\circ ), and sides ( b = 3 ) and ( c = 10 ), you can use the Law of Sines to find the ratio of the lengths of the sides:
[ \frac{a}{\sin(120^\circ)} = \frac{3}{\sin(B)} = \frac{10}{\sin(C)} ]
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Solve for the unknown angles using the given side lengths and the known angle.
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Once you have found the measures of angles ( B ) and ( C ), you can use the fact that the sum of angles in a triangle is ( 180^\circ ) to find angle ( A ).
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Use the Law of Cosines to find the remaining side length. The Law of Cosines states that for any triangle with side lengths ( a ), ( b ), and ( c ), and opposite angles ( A ), ( B ), and ( C ), respectively:
[ c^2 = a^2 + b^2 - 2ab \cos(C) ]
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Plug in the known values to find the length of side ( a ).
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Once you have found all the side lengths and angles, you have solved the triangle.
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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.
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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