April 9th, 2019, 11:32 PM  #1 
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  Square in a right triangle.
Hi, Please solve the question attached in the image file. Thx. 
April 10th, 2019, 03:15 AM  #2 
Senior Member Joined: Feb 2010 Posts: 706 Thanks: 141 
$\displaystyle \dfrac{1092}{\sqrt{3145}} \approx 19.472$

April 10th, 2019, 03:16 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,751 Thanks: 2135 
Are you required to use trigonometry? This can be solved using Pythagoras and the properties of similar triangles, though the working is a bit tedious. What have you tried?

April 10th, 2019, 03:10 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
mrtwhs gave you the solution. WHAT will you do if your teacher asks HOW YOU got the solution? Label the triangle ABC and the square DEFG. So we have 4 similar triangles: ABC, ADG, BEF and CFG. Can you "see" that? 
April 10th, 2019, 03:59 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,751 Thanks: 2135 
The correct solution is (1092/4237)sqrt(3145) m.

April 10th, 2019, 07:03 PM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Hmmm...mrtwhs gets ~19.472, skip gets ~14.454, and I get ~15.273 I used 56 as the hypotenuse (should be ~56.08); shouldn't matter much... I'll have another look tomorrow....musta goofed somewhere... 
April 11th, 2019, 01:19 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,751 Thanks: 2135 
Below is a diagram (to scale) that accurately confirms my answer. SquareInTriangle.PNG 
April 11th, 2019, 03:06 AM  #8 
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  
April 11th, 2019, 03:07 AM  #9 
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  
April 11th, 2019, 03:13 AM  #10 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,826 Thanks: 646 Math Focus: Yet to find out.  

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