Monday, May 21, 2007
posted by faven at 7:47 p.m.
THE COSINE LAW:
IS THE RELATIONSHIP BETWEEN SIDES AND ANGLES IN ANY GIVEN TRIANGLE

THE FORMULA IS:
a 2 = b 2 + c 2 - 2 b c cos(A)
let's say we have a triangle with the side lengths a=10cm b=7cm c=5cm now let's find the largest angle A.
*first step is to set up the formula
a 2 = b 2 + c 2 - 2 b c cos(A)
*then substitute the numbers in, and solve for the largest angle A.
cos (A) = [ 7 2 + 5 2 - 10 2 ] / (2*7*5)

= -13/35
(your calculator will be a big help now)

your answer should be 111.80
so angle A=111.8(rounded to one decimal place)

THINGS TO REMEMBER:
*a,b,c are the side lengths of a triangle .
* A,B,C are the angles.
*the cosine law is often useful when dealing with triangles which are not right angle.
* label your sides and angles so that you don't get confused.
THAT'S WHAT I'VE GOT ON COSINE LAW
SEE YOU GUYS TOMORROW :)
POSTED BY FAVEN.

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Tuesday, May 15, 2007
COSINE LAW
posted by Anonymous at 9:00 p.m.
GENERAL FORM:

a2 = b2 + c2 - 2bc CosA


** Use this formula when you do not have a complete set of ratios ( a length of a side with its corresponding angle ).
Only use this formula (it's confusing & long) ONCE, and then use the sine law or any other formula to help you complete the trig question you have.






















Use the cosine formula given above to substitue in the values:

a2 = b2 ="b + c2 - 2bc CosA
a2 = (7.8)2 + (9.0)2 - 2(7.8)(9.0)Cos112

a2 = 60.84 + 81 - (-52.5947)
a2 = 194.44
a2 = √194.44

a = 13.9




These sites are helpful for extra practice at using cosine law (step-by-step lessons & answers):

http://www.analyzemath.com/Geometry/cosine_law_problems.html
http://www.themathpage.com/aTrig/law-of-cosines.htm

http://dougsimmsonline.googlepages.com/cosinelaw <-- has a vid too!

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