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March 19th, 2018, 09:58 AM  #1 
Newbie Joined: Jan 2018 From: Ontario Posts: 11 Thanks: 0  Can you find side length of a triangle given three angles?
Can you mix dimensionless function or angles to find length in triangles? For example, two sides are composed of a distance of $0.85+0.4=1.25$ and at the same time $0.4=\cos\theta$and the base is $1$? For consecutive numbers or nonconsecutive numbers $x<y<z$, I have the following example: $(((\frac{\sqrt\frac{y}{z}}{(1\frac{x}{z})\times\sqrt\frac{x+z}{zx}})\times\frac{x}{z})+\sqrt\frac{zy}{z})\times((1\frac{x}{z})\times\sqrt\frac{(x+z)}{(zx)})=\sin A$ $(\frac{\sqrt\frac{y}{z}}{(1\frac{x}{z})\times\sqrt\frac{x+z}{zx}})(((\frac{\sqrt\frac{y}{z}}{(1\frac{x}{z})\times\sqrt\frac{x+z}{zx}})\times\frac{x}{z})+\sqrt\frac{zy}{z})\times(\frac{x}{z})=\cos A$ $\sqrt\frac{(zy)}{z}=\cos B$ $\sqrt\frac{y}{z}=\sin B$ $\frac{x}{z}=\cos C$ $((1\frac{x}{z})\times\sqrt\frac{(z+x)}{(zx)})=\sin C$ $(\sqrt{\frac{y}{z}}\times\frac{x}{z})+\sqrt\frac{ zy}{z}\times((1\frac{x}{z})\times\sqrt\frac{(z+x)}{(zx)})=\sin A$ $(\sqrt{\frac{zy}{z}})\times\frac{x}{z}+\sqrt{\frac{y}{z}}\times( (1\frac{x}{z})\times\sqrt\frac{(z+x)}{(zx)})=\cos A$ The following variables $a,b,c$ represent the length of the sides of the triangles. $\frac{\sin A}{\sin C}=a$ $\frac{\sin B}{\sin C}=b$ $\frac{\sin C}{\sin C}=c$ h=altitude $\frac{h_c}{h_a}=a$ $\frac{h_c}{h_b}=b$ $\frac{h_c}{h_c}=c$ $((((\frac{\sin B}{\sin C})\times\cos C)+\cos B)\times\sin C)=\sin A$ $(\frac{\sin B}{\sin C})((((\frac{\sin B}{\sin C})\times\cos C)+\cos B)\times\cos C)=\cos A$ $((((\frac{\sin A}{\sin C})\times\cos C)+\cos A)\times\sin C)=\sin B$ $(\frac{\sin A}{\sin C})((((\frac{\sin A}{\sin C})\times\cos C)+\cos A)\times\cos C)=\cos B$ Last edited by skipjack; March 19th, 2018 at 12:04 PM. 
March 19th, 2018, 02:22 PM  #2  
Global Moderator Joined: Dec 2006 Posts: 20,474 Thanks: 2039  Quote:
If you aren't given the values of the angles A, B and C, the three equations just tell you that c = 1. The above three altitude quotient equations just tell you that c = 1.  
March 19th, 2018, 03:00 PM  #3 
Newbie Joined: Jan 2018 From: Seattle, WA Posts: 20 Thanks: 6 
Angles are insufficient to determine the size of a triangle. 
March 19th, 2018, 03:36 PM  #4 
Newbie Joined: Jan 2018 From: Ontario Posts: 11 Thanks: 0 
An angle has no measurement of units, and for that reason, it is difficult to describe the length of the side of the triangle or the unit doesn't matter.
Last edited by skipjack; March 19th, 2018 at 04:07 PM. 
April 22nd, 2018, 05:11 PM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
For example, every equilateral triangle, whether its sides have length 1 cm or 1000 km, has its three angles the same with measure $\displaystyle \frac{\pi}{3}$.


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algebra, angles, find, length, side, triangle 
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