Pre-Cal Final Exam Review 6

Front

What is the Law of Cosines?

Back

The Law of Cosines states that for any triangle with sides a, b, and c, and angle C opposite side c: c² = a² + b² - 2ab * cos(C). It is used to find unknown side lengths or angles in a triangle.

Front

How do you find the measure of an angle using the Law of Cosines?

Back

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

Front

What is the Law of Sines?

Back

The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant: Sin(A)/a = Sin(B)/b = Sin(C)/c.

Front

How do you use the Law of Sines to find a side length?

Back

To find a side length using the Law of Sines, rearrange the formula: a = (b * Sin(A)) / Sin(B). This allows you to solve for the unknown side.

Front

What is the formula for the Law of Cosines?

Back

c² = a² + b² - 2ab * cos(C) is the formula for the Law of Cosines.

Front

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

Back

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

Front

How do you calculate the distance across a river using the Law of Cosines?

Back

Use the Law of Cosines with the two known sides and the included angle to find the distance across the river.

Front

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

Back

The included angle is the angle between the two known sides. It is crucial for applying the Law of Cosines to find the third side.

Front

What is the cosine of an angle in a right triangle?

Back

In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

How do you find the sine of an angle in a right triangle?

Back

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.