BIG QUESTIONS!
i. Law of Sines
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| https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiACyal4Sb8T5jyRkmCPbk-qx4z2jLUyZS_GUMdSAmq8L2KuTaHNozh28CQyU5mlKiCyLnBwBEtaH9eFrBH1DOeKcocbn65RK7RVzFuMM06Mz_sySjlvD5ra0POAwfNDmjCfUS7otnmolg/s400/Law+of+sines+derivation.JPG |
We need the Law Of Sines because sometimes we aren't working with traingles that are NOT right traingles, that is no 90 degree angle. Normal Trig functions are defined for a right triangle and are not directly useful in solving non-right triangles. However, even though we do not know we can use our handy dandy math skills to figure out the law of sines.
The picture below will demonstrate how to derive the law of sines. On the bottom it says LAW OF SINES IS THEN SIN A/a = SINB/b =SIN C/c !:)
iv. Area Formulas
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| http://www.geometrycommoncore.com/content/unit2/gsrt9/images/notes3.png |
An oblique triangle is a triangle that has all side lengths that are different. To find the area of a triangle we know that its A=1/2BH. However, since the traingle is NOT a right traingle it has no H. If we draw a line representing H(height) and we can use what we know about traingles, such as SINE and the angles and sides we know to find H. In the triangle given above we know that SIN C = h /a . To get H alone we cross multiply to get the eqaution SIN C (a) =h. Now we H so we can sunstitute it back into our original Area Formula of A=1/2BH we get A= 1/2b(asinc). Notice that this formula requires no provided value for the height, the height is being calculated using the sine ratio. CALCULATING AREA THEN REQUIRES TWO SIDES OF A TRAINGLE AND THE INCLUDED ANGEL. SIDE ANGLE SIDE! (SAS)
Resources :)
http://www.geometrycommoncore.com/content/unit2/gsrt9/images/notes3.png
https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiACyal4Sb8T5jyRkmCPbk-qx4z2jLUyZS_GUMdSAmq8L2KuTaHNozh28CQyU5mlKiCyLnBwBEtaH9eFrBH1DOeKcocbn65RK7RVzFuMM06Mz_sySjlvD5ra0POAwfNDmjCfUS7otnmolg/s400/Law+of+sines+derivation.JPG
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