
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 19th, 2018, 10:58 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 01:04 PM. 
March 19th, 2018, 03:22 PM  #2  
Global Moderator Joined: Dec 2006 Posts: 20,269 Thanks: 1958  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, 04:00 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, 04:36 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 05:07 PM. 
April 22nd, 2018, 06:11 PM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
For example, every equilateral triangle, whether its sides have length 1 cm or 1000 km, has its three angles the same with measure $\displaystyle \frac{\pi}{3}$.


Tags 
algebra, angles, find, length, side, triangle 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Triangle side knowing height and angles and...  Azarashi  Trigonometry  9  February 21st, 2017 07:49 AM 
Find the length of the side of a triangle  stgeorge  Geometry  6  November 27th, 2015 02:11 AM 
Finding the length x of the side of a triangle?  matheus  Trigonometry  2  March 31st, 2015 10:06 PM 
Finding Side length of Rhombus inside Isosceles Triangle.  Spaghett  Algebra  8  June 24th, 2011 08:52 PM 
Calculate side from angles and some other sides in triangle  Nicsoft  Algebra  2  January 13th, 2010 01:35 PM 