The Law of Sines and Cosines are fundamental to determine and derive the unknown variables of a triangle (which is not right angled) such as its angles, and sides with some information already given. We are going to prove this theorem right: The Law of SinesThe Law of Sines says that to find the value of an angle or side of a triangle (with either one given), we can calculate the other angle/side by using this formula: sin ß / B = sin α / A
The Law of CosinesThe Law of Cosines says that to find the value of any side with a given angle and other two sides, we use this formula: a^2 = b^2 + c^2 -2bc cos θ. Good luck!!
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Interestingly, I proved the value of pi today! My sister made apple pie (she is, no doubt, an extraordinary baker) today, and I decided, why not incorporate some math to it? So I decided to measure the circumference of the pie tray and then the diameter, to calculate the value of pi. So, I used my earphones as a referent. The total length of the circumference of the pie was equal to about 66 cm. I then measured the diameter of the pie, which turned out to be about 21 cm. When you divide the circumference of any circle by the diameter of the same circle, you get the value of pi! Obviously, due to human error, you can't receive the exact value but I got pretty close: 66cm (circumference measurement) / 21 cm (diameter measurement) = 3.142857... Ta da! So, I basically proved the value of pi which a delicious apple pie as a circle! I know we all know about this, but why can't we try crazy stuff like this! This is super cool! I am a total nerd, I know. Good luck,
Extraneous Solution? Yup, throughout high school math, you will be hearing this term for a loooong time. A super long time. When you are dealing with equations with square roots, you have to always check whether your answer is correct by substituting with the variable. If the solution does not support the equation it is labelled as an extraneous solution. But in this blog post, I will be explaining to you why this happens. Why do these solutions happen to exist? Real Mathematical Reasoning Extraneous Solutions occur because squaring both sides of a square root equation results in 2 solutions (the positive and negative number). Therefore, one of those numbers will be an extraneous solution, or an extra solution which does not fulfill the original equation. For example, x = 4 (original equation) <squaring both sides of the equation> x^2 = 16 x = -4, 4 <substituting x = -4 into the original equation> -4 is not equal to 4 Good luck,
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