sine rule and cosine rule

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 expressed as: c² = a² + b² - 2ab*cos(C).

Front

When should you use the Sine Rule?

Back

Use the Sine Rule when you have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

When should you use the Cosine Rule?

Back

Use the Cosine Rule when you have two sides and the included angle (SAS) or all three sides (SSS) of a triangle.

Front

How do you find a missing angle using the Sine Rule?

Back

To find a missing angle using the Sine Rule, rearrange the formula to isolate the sine of the angle, then use the inverse sine function.

Front

How do you find a missing side using the Cosine Rule?

Back

To find a missing side using the Cosine Rule, rearrange the formula to isolate the side, then solve for its length.

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

What is the formula for finding 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 180-degree rule in triangles?

Back

The sum of the interior angles of a triangle is always 180 degrees.

Front

How can you determine if a triangle is valid using side lengths?

Back

A triangle is valid if the sum of the lengths of any two sides is greater than the length of the third side (Triangle Inequality Theorem).