My Math Forum Pythagorean theorem/Lesson Learned

 Geometry Geometry Math Forum

 February 18th, 2019, 07:55 AM #11 Member   Joined: May 2018 From: Idaho, USA Posts: 54 Thanks: 6 @Denis, I just tried what you said, and now I can finally say I understand the law of cosines. Correct me if I'm wrong, but here's how I understand it. Let's assume there is a scalene triangle. Side a equals 0.732050808. Side b equals 0.896575472. Angle AB equals 75. According to the internet, the law of cosines is c^2 = a^2 + b^2 - 2ab COS(AB). I got the same answer with my method, which is the following: a COS (AC) + b COS (BC) = c c equals one with both methods. Well, I guess great minds think alike, past minds or present minds! The way I understand it, if you have a right triangle, and you have one side, and an angle, you can find another side length by doing the side and cosine by the angle you know. I noticed that when I did my method, the base, which was side C, was divided in two. When I did one side and cosined by the angle, I got two sides of a right triangle, which was half of the scalene triangle. With this method, I easily found the height of the scalene triangle. I did the following. The square root of a^2 - a COS (AC) ^2 I also got the same answer when I used b and BC instead of a and AC. It's all coming together, and I think I am understanding it. Another lesson learned. Jared
February 18th, 2019, 06:02 PM   #12
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Quote:
 Originally Posted by jnicholes I got the same answer with my method
However, you needed to know the other two angles individually, rather than just that angle C = 75$^\circ$.

 February 19th, 2019, 06:45 AM #13 Member   Joined: May 2018 From: Idaho, USA Posts: 54 Thanks: 6 @skipjack you have a point there. I guess depending on the situation, and depending on what information you have , you would have to do one method or another. Heck, you could also use the Law of Sines to find the other angles! Provided you have the information. Anyway, thanks so much for helping me out. Jared
 February 19th, 2019, 08:41 AM #14 Global Moderator   Joined: Dec 2006 Posts: 20,921 Thanks: 2203 You couldn't find the other angles in that way, as you don't initially know the side opposite the given angle.

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