So, this week I am going to explain how to solve triangles using Law of Cosines. This is done with one easy formula. This formula is:
- leg^2=adj. leg^2 + other adj. leg^2 - 2(adj. leg)(other adj. leg) cos(angle between the two adj. legs)
--Now that you know the formula you should be able to solve for these types of trianlges. So I am going to do a few examples.
Example 1: Solve for anlges A and B.
To solve for angle B, 7 and 8 are going to be your adjacent legs. Now your going to plug everything into the formula.
- 5^2=7^2 + 8^2 - 2(7)(8)cos(B)
- B=cos^-1(5^2-7^2-8^2/-2(7)(8))
- B=38.213 degrees
Now to solve for angle A, all you have to do is add up angle B and C and subtract from 180.
- A=81.787 degrees
Example 2: Solve for angles D and E and for side length f.
First lets solve for the side length f. This is very simple. Angle F will be your angle in between of the adjacent legs 9 and 5.
- f^2=9^2 + 5^2 - 2(9)(5)cos(115)
- Take the square root of both sides.
- f=12.001
Now we are going to solve for anlge D. This is going to be just like example 1.
- D=cos^-1(5^2-9^2-12.001^2/-2(9)(12.001))
- D=22.186 degrees
Add up angles D and F and subtract from 180 to find out what angle E is.
- E=42.814 degrees
And that is how you solve problems using Law of Cosines!
--Halie :D
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