Trigonometry Study Sheet
Start with a Triangle
Ask: What kind of triangle is it? (only 2 options)
Right triangle
Non-right triangle
Now ask: are any other angles given or needed?
No?
Pythagorean
Theorem a2 + b2= c2
Yes?
SOH CAH TOA
Now ask: is there a known angle opposite a known side?
Yes?
Sine Law
No?
Cosine Law
So, do you know what to use and how to use it? What are the steps?
Steps for SOH CAH TOA
for sides:
1. Label sides hyp, opp, adj
(opp is the side opposite
the angle given or needed)
Sine Law for sides
We know angle C = 37º, a = 8 and b = 11
The Law of Cosines says: c2 = a2 + b2 - 2ab cos(C)
Put in the values we
know:
Do the 1st & 2nd “chunk”:
2. Decide SOH, CAH or
TOA equation by circling
what is needed and what
is given (eliminate the
equations that have a side
that is not circled)
3. Fill in what is known in
your equation, put the
sinA, cosA or tanA over 1
then do cross multiply and
divide
4. Don't forget units!
SOH CAH TOA for angles
Cosine Law for sides Example:
How long is side "c" ... ?
Subtract:
Take the square root:
x = sin (42) × 11 ÷ 𝑠𝑖𝑛50
= 9.6 units
Sine Law for angles
c2 = 82 + 112 - 2 × 8 × 11 × cos(37º)
c2 = 185 -
140.448…
c2 = 44.44...
c = √44.44 = 6.67 (to 2 decimal
places)
Answer: c = 6.67 units
Cosine Law for angles Example:
What is Angle "C" ...?
In this triangle we know the three sides:
 a = 8,
 b = 6 and
 c = 7.
Use The Law of Cosines (angle version) to find angle C :
Make sure “C” and “c” are the angle and side opposite each other
cos C = (a² + b² - c²)/2ab
= (8² + 6² - 7²)/(2×8×6) do the top, then do the bottom
= 51/96
= 0.53125
C = cos-1(0.53125)
= 57.9° correct to one decimal place.