Law of Sines Flashcard

Front

What is the Law of Sines?

Back

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

Front

How do you solve for a side using the Law of Sines?

Back

To solve for a side using the Law of Sines, rearrange the formula: c = (a * sin(C)) / sin(A) if you know sides a and angle A, and angle C.

Front

What is the first step in using the Law of Sines to solve a triangle?

Back

Identify the known angles and sides. If you have at least one angle and its opposite side, you can use the Law of Sines.

Front

What does it mean if no triangle can be formed with given measurements?

Back

It means that the given angles and sides do not satisfy the triangle inequality theorem or the conditions of the Law of Sines.

Front

What is the triangle inequality theorem?

Back

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

How many triangles can be formed if two angles and a non-included side are known?

Back

There can be either one triangle or no triangle formed, depending on the specific measurements.

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.

Front

If m∠A = 68°, c = 34, and a = 9, how many triangles can be formed?

Back

No triangle can be formed with these measurements.

Front

If m∠A = 110°, c = 19, and a = 32, how many triangles can be formed?

Back

One triangle can be formed with these measurements.

Front

How do you find an unknown angle using the Law of Sines?

Back

Rearrange the Law of Sines to find the sine of the angle: sin(B) = (b * sin(A)) / a, then use the inverse sine function.