Law of Sines and Cosines K

Front

What is the Law of Sines?

Back

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

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. It is expressed as: c² = a² + b² - 2ab*cos(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

How do you determine the angle to walk towards a point using the Law of Sines?

Back

To determine the angle, you can use the Law of Sines to set up a ratio based on the known sides and angles, then solve for the unknown angle.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the formula to find the length of a side using the Law of Sines?

Back

The formula is: a = b * (sin(A) / sin(B)), where a and b are the lengths of the sides opposite angles A and B, respectively.

Tags

CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.10

Front

What is the significance of the angle in the Law of Sines?

Back

The angle is crucial as it helps to relate the sides of the triangle to their opposite angles, allowing for the calculation of unknown lengths or angles.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

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

Back

Use the Law of Cosines when you have two sides and the included angle (SAS) or all three sides (SSS) of a triangle.

Tags

CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.10

Front

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

Back

In a triangle, the larger the angle, the longer the side opposite that angle. This relationship is fundamental in both the Law of Sines and the Law of Cosines.

Tags

CCSS.HSG.CO.C.10

Front

How can you find an unknown angle in a triangle using the Law of Cosines?

Back

You can rearrange the Law of Cosines formula to solve for the angle: C = cos⁻¹((a² + b² - c²) / (2ab)).

Tags

CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.10

Front

What is the first step in solving a triangle using the Law of Sines?

Back

Identify the known sides and angles, and set up the ratio using the Law of Sines to find the unknowns.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the purpose of the Law of Sines in real-world applications?

Back

The Law of Sines is used in navigation, surveying, and various fields of engineering to solve for distances and angles in non-right triangles.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11