Law of Sines and Cosines

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

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: c² = a² + b² - 2ab * cos(C).

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: A = sin⁻¹(a * Sin(B)/b).

Front

How do you find 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 formula for the area of a triangle using the Law of Sines?

Back

Area = (1/2) * a * b * Sin(C).

Front

If angle A = 30 degrees and side a = 10, what is the length of side b if angle B = 45 degrees?

Back

Using the Law of Sines: b = (10 * Sin(45))/Sin(30) = 14.14.

Front

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

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

How do you determine if a triangle is valid with given sides?

Back

A triangle is valid if the sum of the lengths of any two sides is greater than the length of the third side.

Front

What is the significance of the included angle in the Law of Cosines?

Back

The included angle is crucial in the Law of Cosines as it directly affects the calculation of the opposite side.

Front

If two sides of a triangle are known, how can you find the third side?

Back

Use the Law of Cosines: c² = a² + b² - 2ab * cos(C), where C is the included angle.