Sine & Cosine Rule for test review

Front

What is the Sine Rule?

Back

The Sine Rule 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

What is the Cosine Rule?

Back

The Cosine Rule relates the lengths of the sides of a triangle to the cosine of one of its angles. It is given by: c² = a² + b² - 2ab*cos(C).

Front

How do you find an unknown side using the Sine Rule?

Back

To find an unknown side using the Sine Rule, rearrange the formula: a = b * (sin(A) / sin(B)).

Front

How do you find an unknown angle using the Sine Rule?

Back

To find an unknown angle using the Sine Rule, rearrange the formula: A = sin⁻¹(a * (sin(B) / b)).

Front

What is the relationship between the angles and sides in a triangle?

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

Front

When is the Sine Rule applicable?

Back

The Sine Rule is applicable in any triangle, especially when you know two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

When is the Cosine Rule applicable?

Back

The Cosine Rule is applicable in any triangle, particularly when you know two sides and the included angle (SAS) or all three sides (SSS).

Front

How do you find the area of a triangle using the Sine Rule?

Back

The area of a triangle can be found using the formula: Area = 1/2 * a * b * sin(C), where a and b are two sides and C is the included angle.

Front

What is the significance of the angle opposite the longest side in a triangle?

Back

The angle opposite the longest side is the largest angle in the triangle, and it is crucial for applying the Sine and Cosine Rules.

Front

How do you solve for a missing side using the Cosine Rule?

Back

To solve for a missing side using the Cosine Rule, rearrange the formula: c = √(a² + b² - 2ab*cos(C)).