When To Use What Trig?

WHEN TO USE WHAT?

SOH CAH TOA:  These laws can be used when you have a right triangle, you have one angle, and one side (for the same triangle).

“Opposite, Adjacent and Hypotenuse” refer to the length of the side relative to θ (Theta). To use this formula you must have two of the variables in the equation.

Sin θ = Opposite/Hypotenuse:

Cosine θ = Adjacent/Hypotenuse

Tangent θ = Opposite/Adjacent

triangle showing Opposite, Adjacent and Hypotenuse

 

Sine Law: Sin A/a = Sin B/ b = Sin C/c: This law is used for looking for a side or an angle that is missing on a non-right triangle.

A, B, C are representative of the angles on a triangle. Any three letters in alphabetical order may be used to represent the angles.

a, b, c are representative of the side lengths of a triangle –the same rule applies to small letters that applied to capitals.

This law can be used to find the Ambiguous Case on a triangle (a triangle in which two side lengths are given and one angle opposite to a side is given). The Ambiguous Case is written as A-S-S most often, “S” means side and “A” means angle.

This law  may only be used when either two side lengths and one opposite angle is given, or when two angles and one opposite side is given.

triangle

 

Cosine Law: a^2= b^2 + c^2 – 2bc * Cos A : This law can be used to find a side or an angle missing on a non-right triangle.

The letter rules that applied to Sine Law apply here.

This rule may be used when two opposite sides and one angle in between is given, or when three of the variables in the equation are given. This law is often written as S-A-S.

The Cos A may be replaced by either Tangent A or Sine A.

 

trig cos rule example

 

Reflection on Math 10:

In Math 10 you learned how to use SOH CAH TOA to find the sides of a right triangle, this year it is an expansion on every thing. This year we gained the skills to solve non right triangle. d