Law of Sines and Law of Cosines Remediation

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 its opposite angle is constant for all three sides and angles in the triangle.

Front

What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles, expressed as: c² = a² + b² - 2ab * cos(C).

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, use the formula: a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the sides opposite angles A, B, and C respectively.

Front

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

Back

To find an angle using the Law of Sines, rearrange the formula: sin(A)/a = sin(B)/b = sin(C)/c, and use the inverse sine function.

Front

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

Back

In any triangle, the larger the angle, the longer the side opposite that angle.

Front

What is the formula for the area of a triangle using the Law of Sines?

Back

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

Front

How can the Law of Cosines be used to find a side?

Back

To find a side using the Law of Cosines, use the formula: c = √(a² + b² - 2ab * cos(C)).

Front

How can the Law of Cosines be used to find an angle?

Back

To find an angle using the Law of Cosines, rearrange the formula: cos(C) = (a² + b² - c²) / (2ab).

Front

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

Back

The angle opposite the longest side in a triangle is the largest angle.

Front

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

Back

The angle opposite the shortest side in a triangle is the smallest angle.