Law of Sines and Law of Cosines Review

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: Sin(A)/a = Sin(B)/b = Sin(C)/c.

Front

What criteria can be used to apply the Law of Sines?

Back

The criteria for using the Law of Sines are SSA (Side-Side-Angle), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side).

Front

When would you use the Law of Cosines instead of the Law of Sines?

Back

The Law of Cosines is used when you have SAS (Side-Angle-Side) or SSS (Side-Side-Side) configurations in a triangle.

Front

What is the formula for the Law of Cosines?

Back

The Law of Cosines states that c² = a² + b² - 2ab * cos(C), where a, b, and c are the sides of the triangle and C is the angle opposite side c.

Front

If angle A = 30° and side a = 10, what is the value of Sin(A)?

Back

Sin(30°) = 0.5.

Front

How do you find the length of a side using the Law of Sines?

Back

To find a side using the Law of Sines, rearrange the formula: a = (b * Sin(A)) / Sin(B).

Front

What is the relationship between the angles and sides in a triangle according to the Law of Sines?

Back

The angles opposite larger sides are larger, and the angles opposite smaller sides are smaller.

Front

If you know two angles of a triangle, how can you find the third angle?

Back

The third angle can be found using the formula: Angle C = 180° - (Angle A + Angle B).

Front

What is the significance of the SSA condition in the Law of Sines?

Back

The SSA condition can lead to two possible triangles, one triangle, or no triangle at all, making it ambiguous.

Front

What does the acronym SOH-CAH-TOA represent?

Back

SOH-CAH-TOA is a mnemonic for remembering the definitions of sine, cosine, and tangent: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.