My Math Forum Square in a right triangle.

 Trigonometry Trigonometry Math Forum

April 9th, 2019, 11:32 PM   #1
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Square in a right triangle.

Hi,

Please solve the question attached in the image file.

Thx.
Attached Images
 maths_q_trig.jpg (16.1 KB, 16 views)

 April 10th, 2019, 03:15 AM #2 Senior Member     Joined: Feb 2010 Posts: 711 Thanks: 147 $\displaystyle \dfrac{1092}{\sqrt{3145}} \approx 19.472$ Thanks from happy21 and topsquark
 April 10th, 2019, 03:16 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2219 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? Thanks from topsquark
 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? Thanks from happy21 and topsquark
 April 10th, 2019, 03:59 PM #5 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2219 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: 20,969 Thanks: 2219 Below is a diagram (to scale) that accurately confirms my answer. SquareInTriangle.PNG Thanks from happy21
April 11th, 2019, 03:06 AM   #8
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Quote:
 Originally Posted by mrtwhs $\displaystyle \dfrac{1092}{\sqrt{3145}} \approx 19.472$

April 11th, 2019, 03:07 AM   #9
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Quote:
 Originally Posted by Denis 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?
True and thanks. But plz elaborate two three steps.

April 11th, 2019, 03:13 AM   #10
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Quote:
 Originally Posted by Denis Hmmm...mrtwhs gets ~19.472, skip gets ~14.454, and I get ~15.273
So just take the average!

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