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 June 14th, 2016, 01:27 PM #1 Newbie   Joined: Jun 2016 From: home Posts: 1 Thanks: 0 Triangle inside another problem Hi I have a problem which I am sure is simple, but I can't get it right. Given is beta, x, and y. Required is Phi. Can you help? Last edited by skipjack; June 14th, 2016 at 01:43 PM. June 14th, 2016, 02:55 PM #2 Global Moderator   Joined: May 2007 Posts: 6,806 Thanks: 716 Notation: u=long hypotenuse, v=short hypotenuse, w=vertical side of triangles. b=beta, p=phi 1)y/u=sinb or u=y/sinb. 2)w=ucosb. 3)(y-x)/w=tan(b-p). 4)p=b-arctan(b-p)=b-arctan((y-x)/w). Carry out steps above in order. June 14th, 2016, 04:07 PM #3 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Let $h$ be the height of the triangle. Then $$h=\dfrac{y}{\tan\beta},\quad\phi=\beta-\tan^{-1}\left(\dfrac{y-x}{h}\right)$$ June 14th, 2016, 04:25 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 $\phi$ = tan$^{-1}$(sin(β)cos(β)/(y/x - sin²(β))) by mathman's method, but greg1313's way of writing it is simpler and implies $\phi = \beta - \tan^{-1}((1 - x/y)\tan\beta)$. Tags inside, problem, triangle Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Abdus Salam Geometry 2 July 6th, 2015 12:18 PM matisolla Geometry 4 May 15th, 2015 04:01 AM Brolie Number Theory 3 August 31st, 2014 07:07 AM chameleojack Calculus 6 May 11th, 2014 07:29 PM Spaghett Algebra 8 June 24th, 2011 07:52 PM

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