Non-right Triangle Trigonometry Flashcards
What are the formulas we can use to find missing sides and angles of non-right triangles?
Sine Rule
and
Cosine Rule
What is the sum of all the angles in a triangle?
180 degrees
If you are given two angles in a triangle, how can you find the third missing angle?
1) Add the Given Angles.
2) Subtract the sum from 180°.
Can we use SOH-CAH-TOA for the following triangle?
NO! This triangle is NOT a right triangle. We must use either the sine or the cosine rule
In the Sine Rule and Cosine Rule formulas, what do the upper case letters represent? What do the lower case letters represent?
upper case letters are angles
lower case letters are sides
How should a non-right triangle be labelled?
If an angle is labelled as capital “A,” then little “a” is always used for the side opposite (directly across from) it. Angle “B” is opposite side “b,” and so on.
ALWAYS label ALL sides and angles. People make silly mistakes by plugging in the wrong values into the sine and cosine rules because they got their sides and angles confused.
Suppose you have a problem with the following pairs:
Given pair: a complete side and angle pair (you have the value for an angle and its opposite side)
Incomplete Pair: a pair where you are given an angle but trying to find the opposite side
What formula should you use?
Sine Rule
Suppose you have a problem with the following pairs:
Given pair: a complete side and angle pair (you have the value for an angle and its opposite side)
Incomplete pair: a pair where you are given a side but trying to find the opposite angle
What formula should you use?
The reciprocal (flipped) version of the Sine Rule
(This version is not in the formula chart but it is just a flipped version of what is in the formula chart)
Given: An angle sandwiched between two sides, a.k.a. Side, Angle, Side (SAS)
Find: Missing Side
Which formula should you use?
Use the Cosine Rule (Missing Side Version)
Given: Side, Side, Side (SSS)
Find: Missing Angle
Which formula?
How could you rewrite this cosine rule to find an angle X in triangle XYZ?
Just replace “C” with the angle you are looking for (in this case “X”). Then replace the little “c” with little “x.”
Finally, replace “a” and “b” with the other two sides (in this case “y” and “z”)
How could you rewrite this formula to find side p in triangle PQR?
Just replace the little “c” with the side you are looking for (in this case “p”). Then replace the big “C” with big “P”.
Finally, replace the little “a” and “b” with the other two sides (in this case, “q” and “r”)
What calculator mode does your calculator need to be on in order to solve sine rule and cosine rule problems?
DEGREES MODE!
What’s the cheat to know which angle goes in the cosine rule?
The angle must be “sandwiched in” between two known sides (inscribed).
Can I use A = bh/2 to find the area of this triangle?
No. We don’t have the vertical height. For non right-angle triangles use:
How do you find the area of a triangle using the area formula for nonright triangles?
The area of a triangle is half of the product of two sides and the sine of the included angle.
How would you find b?
How would you find angle B?
What rule would you use for this trianlge?
What is an “angle of depression”?
It’s the angle between the ceiling and a downward line.
What is an “angle of elevation”?
It’s the angle between the floor and an upward line.
What are angles of elevation and depression?
