Saturday, September 22, 2012
Link to a post about the Law of Cosines and some practice problems
Here is a post about Law of Cosines from 2011.
Here are examples with two side lengths a and b and the measure of between them, gamma, in degrees. Use these to find the length of c exactly and rounded to four places after the decimal.
a = 3, b = 4, gamma = 45°
a = 3, b = 4, gamma = 90°
a = 3, b = 4, gamma = 135°
Answers in the comments.
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a = 3, b = 4, gamma = 45°
ReplyDeletec² = 3² + 4² - 2(3)(4)cos45°
c² = 9 + 16 - 24sqrt(2)/2
c² = 25 - 12sqrt(2)
c = sqrt(25 - sqrt(2))
c ~= 4.8565
a = 3, b = 4, gamma = 90°
c² = 3² + 4² - 2(3)(4)cos90°
c² = 9 + 16
c² = 25
c = 5
This is the famous 3-4-5 triangle.
a = 3, b = 4, gamma = 135°
c² = 3² + 4² - 2(3)(4)cos135°
c² = 9 + 16 + 24sqrt(2)/2
c² = 25 + 12sqrt(2)
c = sqrt(25 + sqrt(2))
c ~= 5.1395
Note: since a and b don't change but the angle gamma does, we should expect the side length c to get longer as gamma approaches 180°, when c would equal 7.