This week in math we learned how to use the Sine and Cosine law. I choose this skill because it was an improved version of past formulas that used trignometric ratios and inverse trigonmetric ratios and could apply to all triangles. This is an important skill to finding the length and angles of any triangle in order to solve it not just right angle ones.

Sine Law (Law of Sines)

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. This can be written as:

Steps to Use the Sine Law:

1. Identify the known values in the triangle (sides and angles).
2. Set up the ratio according to the Sine Law.
3. Solve for the unknown value.

Example:

Given triangle , where:
–
–
–

Find side .

Solution:

1. Identify the known values:
–
–
–

2. Set up the ratio:

3. Plug in the known values:

4. Solve for \( b \):

Cosine Law (Law of Cosines)

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It can be written as:

Steps to Use the Cosine Law:

1. Identify the known values in the triangle (sides and angles).
2. Set up the equation according to the Cosine Law.
3. Solve for the unknown value.

Example:

Given triangle ( ABC ), where:
–
–
–

Find side c.

Solution:

1. Identify the known values:
–
–
–

2. Set up the equation:

3. Plug in the known values:

These examples demonstrate how to apply the Sine and Cosine Laws to find unknown sides or angles in a triangle.