Transcript 8.6 Law of Cosines - Fay's Mathematics [licensed for non

8.6 Law of Cosines
• The Law of Cosines is more difficult to remember. It
is also a formula that is much more difficult to
derive/create. Remember these formulas are not
must plucked out of the air, there is algebra behind
each and every formula. Formulas are shortcuts
that we recognize after doing a particular style of
problem a numerous amount of times, the formula
then allows us to complete such problems in a
much quicker (sometimes more cryptic) method.
One formula we know pretty well is the quadratic
formula, its pretty cryptic, however it’s a shortcut
that allows us to factor quadratics at a much more
rapid pace..
• This is how I remember the formulas. The first
letter and last letter are always the same.
• The middle numbers are then the left over letters.
And their order does not matter. Must remember
the operations of squaring and adding, and then
subtracting 2 times their product.
• The Law of Cosines allows us to deal with non-right
triangles that information is provided for in the
form of SAS or SSS. Identify which of the 2
orientations is provided in the example and then
solve the triangle.
Searching for b. So start with the
formula, b2=a2+c2-2acCos(B)
Now that you know b, can you find the other angle measurements? Are
there multiple methods to find m<A and m<C? Should they all give back the
same values?
Finishing off the triangle
• Once you start finding out more things about
your triangle then that usually opens the door
for you to use different techniques/methods
to find the remaining information. If I have to
use Law of Cosines for something, I usually
then solve the remaining parts using the Law
of Sines simply because I think that the math
for the Law of Sines is easier to work with. It
is ultimately your choice.
Use Law of Cosines
Find the measure of angle T.
Then find the measure of angle V.
How long is c?
•
The N 75o E is a tricky concept sometimes to think about when you get into precalculus and physics we will discuss how “bearings” generally work. For questions
like this I will provide you the (75o east of north) description