This week in pre calculus 11, we studied our last unit on trigonomitry, which was an add on to what we’ve learned and covered in math 10, but unlike math 10, we learned how to find the angles and sides of a triangle without a 90° angle (right triangle), through sine law and cosine law.

Review:

Soh- Sine= opposite/hypotenuse

Cah- Cosine= adjacent/hypotenuse

Toa- Tangent= opposite/ adjacent

Sides of a right triangle: a² + b² = c²

New:

CAST law explains which functions are positive in the 4 quadrants

The special triangles with a 90° angle will give us the ratios

Sine law:

Finding the Sides: a/sinA = b/sinB = c/sinC 

Finding the Angles: sinA/a = sinB/b = sinC/c

Take the given triangle and plug the numbers into the sine law to find the two fractions that give you 2 angles and 1 side or vice versa, and isolate the missing variable.

-Uppercase letters stand for the angles of the triangle

-Lowercase letters stand for the sides of the triangle

-All three angles add up to make 180°

example:

steps)

• find the missing angle(we can easily find it because we are given 2 angles)
• take two of the fractions that make up the sine law(one always has to have both the angle and side length)
• isolate side b

Cosine Law: can be used when you have 2 sides and an angle or 3 sides

a2 = b2 + c2 – 2bc cos A

b2 = a2 + c2 – 2ac cos B

c2 = a2 + b2 – 2ab cos C

or  

Isolate the missing variable.

example:

Steps)

• plug in the numbers into the equation
• simplify the equation
• isolate cos C
• use the inverse cosine to fine the angle