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August 5th, 2018, 11:50 PM  #1 
Senior Member Joined: Nov 2015 From: USA Posts: 107 Thanks: 6  Odd answers on solving triangles
I'm trying to figure out the length of the hypotenuse as the angle grows from 90 to 180 degrees. However, the results I'm getting say that 180 degrees has a shorter length than 135 degrees, which is wrong. At 180 degrees, Side + Side = Hypotenuse. (it is just a line, with two short lengths equaling the long length) I started with side lengths of 3 and 4, but at 135 degrees, the math says the hypotenuse is 6.997, and at 180 degrees it says 6.273. I can draw it on paper and see how wrong this is. But as near as I can tell, I'm doing the steps right, (b*b)+(c*c)(2*b*c)*(cos(angle)) (3*3)+(4*4)(2*3*4)*(cos(180)) do brackets (googling the cosine) (9)+(16)(24)*(0.59846006905) enter into calculator and get 39.3630416572 root 6.2739972630851537533570604650014 double checking the calculator 9+16(14.3630416572) 25(14.3630416572) 39.... So I'm still getting the wrong answer. What am I missing? I know that a triangle with no area (the angle across from the hypotenuse being 180 degrees), with the short sides of 3 and 4 has a hypotenuse of 7. But I've done this with 135 degrees as well (90 plus 45. Also drawn and measured as shorter than 6.997), and still get an incorrect answer. Is google wrong on the cosine, or do I need to use something different for angles over 90 degrees like with sine? 
August 6th, 2018, 01:00 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond 
cos(180$^\circ$) = 1. The calculator you are using is giving results for a radian measure.

August 6th, 2018, 01:35 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,380 Thanks: 2011 
Agreed. Google seems to understand cos(180 deg), so try that instead.

August 6th, 2018, 01:35 AM  #4 
Senior Member Joined: Nov 2015 From: USA Posts: 107 Thanks: 6 
Ah, radians. Thank you.

August 9th, 2018, 01:49 PM  #5 
Newbie Joined: Jul 2015 From: Jonesborough, TN Posts: 3 Thanks: 0 
It's not a triangle if the length of two sides are not greater than the third side. Triangle inequality theorem.... 
August 12th, 2018, 03:06 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Also if a triangle has an angle greater than 90 degrees, it is NOT a right triangle so does NOT have a "hypotenuse". You appear to have an obtuse triangle and are trying to determine the length of the side opposite the obtuse angle.

August 18th, 2018, 04:50 PM  #7  
Senior Member Joined: Nov 2015 From: USA Posts: 107 Thanks: 6  Quote:
But a much simpler way of describing it was already given, and seemingly understood.  

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