My Math Forum Solving triangles with the given formation using law of sines and cosines

 Trigonometry Trigonometry Math Forum

 November 12th, 2017, 11:03 AM #1 Newbie   Joined: Oct 2017 From: cali Posts: 8 Thanks: 0 Solving triangles with the given formation using law of sines and cosines So when doing these problems, I can simply just use law of cosines and solve for side b, which is 4.5. That is simple enough to me; however, this is where I start randomly having trouble. I now use law of sines, so here I'll do sin B (angle)/side b = to sin alpha (angle a) over 6.8. I get sin alpha by itself and get 6.8sin10.5/4.5 on the other side, and then find the inverse which gets me 16, which isn't the right answer. However, when I do the same thing except with sin y (angle c) / 2.4 which I show below the line, I get the right answer which is 5.6 for angle c. My question is does it matter which angle I use when using law of sines? because I'm getting different answers using both, when I was under the impression that I could've solved for either of them as long as I had both a side and an angle for one part of the triangle. Last edited by skipjack; November 12th, 2017 at 12:24 PM.
 November 12th, 2017, 12:36 PM #2 Global Moderator   Joined: Dec 2006 Posts: 19,870 Thanks: 1833 Note that sin(16°) and sin(164°) have the same value. Once you know the shortest side, you know that the angle opposite it must be acute.
 November 12th, 2017, 12:50 PM #3 Newbie   Joined: Oct 2017 From: cali Posts: 8 Thanks: 0 So what you're saying that both ways are correct? But how so? Last edited by skipjack; November 12th, 2017 at 07:59 PM.
 November 12th, 2017, 08:23 PM #4 Global Moderator   Joined: Dec 2006 Posts: 19,870 Thanks: 1833 You can get b = 4.46 (to 3 significant figures), then arcsin(sin(10.5°)*2.4/4.46) = 5.63° (to 3 s.f.), and so $\alpha$ = 180° - 10.5° - 5.63° = 163.9° (approximately), rather than 16.1°. The angle opposite the shortest side is acute (for any triangle). The angle opposite the longest side is obtuse in this problem, but isn't obtuse for every triangle. Thanks from materialartist09

 Tags cosines, formation, law, sines, solving, triangles

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Ala Trigonometry 2 May 13th, 2017 02:10 PM njuice8 Calculus 1 May 19th, 2013 10:01 PM jkh1919 Algebra 1 November 26th, 2011 02:27 PM molokach Algebra 19 February 25th, 2011 05:02 PM Stephanie7 Algebra 1 April 19th, 2009 02:04 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top