Law of Cosines

Front

What is the Law of Cosines?

Back

The Law of Cosines states that for any triangle with sides a, b, and c, and angles A, B, and C opposite those sides, the following relationship holds: c² = a² + b² - 2ab * cos(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

When would you use the Law of Cosines instead of the Law of Sines?

Back

The Law of Cosines is used when you have either SSS (three sides) or SAS (two sides and the included angle) to find unknown angles or sides.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the formula for the Law of Cosines?

Back

c² = a² + b² - 2ab * cos(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What criteria must be met to use the Law of Cosines?

Back

The criteria for using the Law of Cosines are SSS (three sides known) or SAS (two sides and the included angle known).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

Solve for angle C using the Law of Cosines: a=5, b=7, c=10.

Back

C = cos⁻¹((a² + b² - c²) / (2ab)) = cos⁻¹((5² + 7² - 10²) / (2 * 5 * 7)) = 60°.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

If a triangle has sides of lengths 8, 15, and 17, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem: 8² + 15² = 17².

Tags

CCSS.8.G.B.8

Front

What is the relationship between the angles and sides in a triangle according to 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.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

How do you find the length of side a using the Law of Cosines?

Back

a = √(b² + c² - 2bc * cos(A)).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the significance of the Law of Cosines in solving triangles?

Back

The Law of Cosines allows for the calculation of unknown sides or angles in triangles that are not right-angled.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

If angle A = 45° and sides b = 10 and c = 12, how do you find side a?

Back

Use the formula: a² = b² + c² - 2bc * cos(A). Calculate a = √(10² + 12² - 2 * 10 * 12 * cos(45°)).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11