9. Finding a Side
You have one sprinkler and a plant that goes with it. You know that the plant is 2 feet tall and the sprinklr sprays 4 feet. The plant meets he ground at a 35° angle and the sprinkler meets the ground at a 42°. How far should they be set apart so that the water reaches the plant?
Since you know two angles you can find the third angle which is 103°. You put 103° in the 'C' for Cos.
The formula of Law of Cosines: c^2=a^2+b^2-2abCosC
The substitute for this question is c^2=2^2+4^2-2(2)(4)Cos103
When you do the math you get:c^2=20-16Cos103
This is: c^2=23.59
You then find the square root of 23.59.
So c≈4.86
The formula of Law of Cosines: c^2=a^2+b^2-2abCosC
The substitute for this question is c^2=2^2+4^2-2(2)(4)Cos103
When you do the math you get:c^2=20-16Cos103
This is: c^2=23.59
You then find the square root of 23.59.
So c≈4.86
10. Finding an angle
You have a plant that you are desperately trying to grow. The plant sits 13 inches away from the window, the suns ray from inside the window to the plant is 15 inches, and the ray comes in 12 inches from the base of the plant. What degree is the suns ray?
Label 13 as A, 15 as B and 12 as C because it is opposite to theta and Law of Cosines tells you what C is.
When you put it in the formula you get: 12^2=13^2+15^2-1(13)(15)CosC
After you square and multiply you get: 144=169+225-390CosC
You then subtract both sides by 225 giving you: -81=169-390CosC
Then subtract both sides by 169: -250=-390CosC
Now divide both sides by 390 which leaves: 25/39=CosC
25/39 is your ratio and since you're finding an angle you use Cos inverse: cos^-1(25/39)=c
C=50.13
When you put it in the formula you get: 12^2=13^2+15^2-1(13)(15)CosC
After you square and multiply you get: 144=169+225-390CosC
You then subtract both sides by 225 giving you: -81=169-390CosC
Then subtract both sides by 169: -250=-390CosC
Now divide both sides by 390 which leaves: 25/39=CosC
25/39 is your ratio and since you're finding an angle you use Cos inverse: cos^-1(25/39)=c
C=50.13
The sun's degree is 50.13°