[.OMG KRAKKEN.]
What is the Pythagorean Theorem? Give two examples where this theorm would be helpful in a real life situation.
If the two legs of a 45-45-90 triangle are each 12 feet long, what is the exact length of the hypotenuse? Can this eaxcat length be expressed in decimal form? Why or why not?
What do the terms since, cosine, and tangent refer to? The tangent of qa 40 degree angle in any right triangle gives you the result of 0.839. Why do you get this same result for the tangent of ang 40 degree angle in a right triangle, regardless of how large the triangle actually is?
Pythagorean theorem is a^2 + b^2 = c^2. It is used in surveying, finding apparent size, finding shortest distances in maps, etc. It is in our stickies.
Again, this is in our stickies. This is a 45-45-90 triangle, therefore the sides are in a ratio of 1-1-rt 2 where rt is the hypotenuse. So it's 12-12-12rt2
You can also do this using the Pythagorean theorem. 12^2+12^2=rt288=12rt2. This cannot be expressed in decimal form because rt2 is irrational.
Again, go to the sticky. sine is opp/hyp. cos is adj/hyp. tan is sin/cos = opp/adj. You get that result for tan 40 in right triangles because it is the ratio of opposite side to adjacent. Since it is a ratio, terms cancel out and you will get that decimal number (even though that's not what it really is because it is irrational). It is also because similarity of triangles does not affect their angle measure.
For future reference, please check out the sticky with helpful math formulas and try to solve some of these by yourself. All you need to do is think a little bit.
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