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Math 10/11Triangles and Trigonometry 2left28638500We learned a few things to find the missing information about triangles.This math was used to figure out a great many mysteries of science.ReviewWhat does a2+b2=c2 help us find?Does it matter which sides you use as a2 or b2?How is trigonometry different than a2+b2=c2?Why is Tan 45o a good problem to check your calculator or memory?What does the above problem mean?What do the inside angles of a triangle add up to?Can you figure out the missing angle of a triangle if you know the other two?3964305850900Trigonometry using Tan (Tangent)To review, practice using your calculator and find Tan (45o).Do the reverse find 1(Tan-1). It should be 45oWhy is this? Looking at this diagram can you tell?You can see that if an angle changes the lengths of the sides change. Play with this tool and see how the different sides change in certain ways.left317500For the tan ratio you can you see that three different sized triangles can have the same angle.So when we say:Tan(angle “c”) is Opposite Adjacent What matters is the ratio or Opposite ÷ Adjacent.Try this for the triangles on the left: 3÷6= 0.5, 2÷4=0.5, 1÷2=0.5So, each of the triangles have the same angle. (27o).To review: to talk about these problems we need names for these sides.left27241500The long side is Hypotenuse, but the other two it depends which angle you’re using.Here you can see the same triangle twice and the angle changes which sides are Opposite and Adjacent.Opposite is the farthest sideAdjacent means beside, so it is the line beside that isn’t the long side.Hypotenuse is the long side.For this week: write which are the sides for the following triangles:You can answer by saying: 1. Side ZX is the adjacent, ZY is opposite and XY is hypotenuse.Part 2left416966 318897057023000Of course, sometimes you don’t know the Opposite and the Adjacent. (You could figure it out using: a2+b2=c2). If you do need to find the Opposite or the Adjacent and you know the Hypotenuse. In these two cases you might have a situation where Tan wouldn’t work. To avoid more work you can use a different ratio Sin (Sine) or Cos (Cosine).Sine and CosineThese two ratios work the same as Tan. You just use them when you know the hypotenuse and don’t know one of the other sides.To remember which is which: People memorize the mnemonic: SOHCAHTOA, although honestly you can look it up.Just like with the Tan of 45oSine and Cosine have angles that work out with whole numbers.Sin of 30o is 0.5Cos of 60o is also 0.5 (Each of these is measuring the same triangle).Try with your Calculator to reproduce these numbers. Use et 30o and get 0.5 (You probably put 30 then Sin)Use 0.5 to get 30o (0.5 Sin-1)Try the same with 60 and Cos.You’ve now practiced Sin Cos and Tan. You should be able to figure out any missing information about any triangle. Try at least 2 of these for homework. It should be solves with Sin. The second needs a different ratio. (Start with identifying Opposite, Adjacent and Hypotenuse).EXTENSION:Look at these notes that go a little deeper. There is a program that allows you to move a triangle to look at any angle. : If the above problems are too easy, try some of these real-world problems.367220569850040894013843000 2.3793492746253. 43891247802004. ................
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