Law of Sines and Cosines Review

Front

What is the Law of Cosines formula?

Back

c² = a² + b² - 2ab cos(C)

Front

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

Back

Use the formula: \( \frac{\sin A}{a} = \frac{\sin Z}{z} \) and solve for Z.

Front

What is the Law of Sines formula?

Back

\( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \)

Front

How do you find side c using the Law of Sines?

Back

Use the formula: \( \frac{\sin 41}{19} = \frac{\sin 75}{c} \) and solve for c.

Front

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

Back

The ratio of a side length to the sine of its opposite angle is constant for all three sides.

Front

What is the purpose of the Law of Cosines?

Back

To find a side or angle in a triangle when two sides and the included angle are known, or when all three sides are known.

Front

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

Back

Use the formula: \( \frac{\sin 44}{26} = \frac{\sin A}{23} \) and solve for A.

Front

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

Back

Angle C is the angle opposite side c, which is used in the formula to relate the sides of the triangle.

Front

What is the formula to find the length of side XZ using the Law of Cosines?

Back

Use the formula: \( XZ^2 = a^2 + b^2 - 2ab \cos(C) \) where a and b are the other two sides.

Front

What is the first step in applying the Law of Sines?

Back

Identify a known angle and its opposite side to set up the ratio.