Download Notes: Trigonometry basics Right triangles – A right triangle (like the

Notes: Trigonometry basics
Right triangles –
A right triangle (like the one in the figure below) has one angle that is 90°. The other
two angles are always less than 90 ° and together add up to 90°. Note that the
triangle below has 3 angles a, b and c and 3 sides, A, B, and H, and 3 angles a, b, and
c. The side "opposite" an angle (in this case) is labeled with a capital letter
corresponding to the label on the angle. The side opposite the right angle, H, is
always the longest side and is called the hypotenuse.
(draw triangle here)
Hypotenuse is always the longest side – opposite the largest angle.
Convention: sides are lower case letters and angles are upper case letters.
Opposing pairs match A-a B-b, etc. This way everyone knows what you are talking
about
Remember the Pythagorean theorem:
a 2  b 2  c2
Trigonometry ratios for right triangles only:
sin 
opposite
hypotenuse
SOH
cos 
adjacent
hypotenuse
CAH
tan 
opposite
adjacent
TOA
1
Examples:
Note: these ratios have no units: 2m / 4m
We’ll be using degrees and not radians in this class.
If you have a triangle, you have three angles and three sides. If you are given three
of these in any combination except for three angles, you can calculate the remaining
parts. In a right triangle, you already know one angle – 90 degrees! You only need
two others: two sides or an angle and a side.
Use the Pythagorean theorem and sin, cos and tan to determine the rest of the
information.
Practice with trig functions here:
1
1
1
Inverse trig functions: sin x cos x tan x
When you have the ratio and need the angle associated with it.
Two special cases that you might see:
Also, 3-4-5 triangles – or multiples of these
Practice – Right triangle trig worksheet
2
What if you have triangles that are not right? Obtuse or acute triangles?
Introduction of Law of Sines:
sin A sin B sinC


a
b
c
or
a
b
c


sin A sin B sinC
when do you use these?
1. When you are given an opposing pair. (otherwise, use LOC)
2. use the first when you are finding an angle, use the second when
you are finding a side – less algebra!
Law of Sines packet – examples
What if you don’t have an opposing pair?
Have to use the Law of Cosines – more difficult, so use LOS if you can!
a2  b2  c2  2bccos A
b2  a2  c2  2accos B
c2  a2  b2  2abcosC
a and A are opposing side / angle pair
b and B are opposing side / angle pair
c and C are opposing side/ angle pair
3