Law of Sines

Front

What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides and angles of the triangle. It can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

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In the context of the Law of Sines, what does SSA stand for?

Back

SSA stands for Side-Side-Angle, which is a condition in triangle problems where two sides and a non-included angle are known. This case can lead to ambiguous solutions.

Front

What is meant by 'ambiguous case' in the Law of Sines?

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The ambiguous case occurs when two sides and a non-included angle (SSA) are known, which can result in zero, one, or two possible triangles.

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What is the relationship between angles B1 and B2 in a 2-solution case?

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In a 2-solution case, angles B1 and B2 are supplementary angles, meaning they add up to 180 degrees.

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How do you determine the number of solutions in an SSA case?

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To determine the number of solutions in an SSA case, analyze the given sides and angle. If the known angle is acute and the opposite side is shorter than the adjacent side, there may be two solutions. If the opposite side is longer, there is one solution. If the opposite side is shorter than the height of the triangle, there are no solutions.

Front

What is the formula to find the length of a side using the Law of Sines?

Back

To find the length of a side using the Law of Sines, use the formula: a = b * (sin(A) / sin(B)), where a and b are the lengths of the sides, and A and B are the angles opposite those sides.

Front

What is the significance of the angle sum property in triangles?

Back

The angle sum property states that the sum of the interior angles of a triangle is always 180 degrees. This property is essential when using the Law of Sines to find unknown angles.

Front

What conditions must be met to use the Law of Sines?

Back

The Law of Sines can be used when you have either: 1) AAS (Angle-Angle-Side), 2) ASA (Angle-Side-Angle), or 3) SSA (Side-Side-Angle) cases.

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What is the result when given side a, side b, and angle C in terms of the Law of Sines?

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When given side a, side b, and angle C, the Law of Sines cannot be applied directly to find the remaining angles or sides, as this configuration does not provide enough information to determine a unique triangle.

Front

How do you round the value of a side or angle in triangle problems?

Back

When rounding the value of a side or angle in triangle problems, follow the standard rounding rules: if the digit after the rounding place is 5 or greater, round up; if it is less than 5, round down.