My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 2nd, 2013, 04:33 PM   #1
Senior Member
 
Joined: Dec 2012

Posts: 450
Thanks: 0

find the angles and sides of the triangle

Can you find all other measures of a triangle, if the three sides(SSS) or 2 sides and the included angle (SAS) OR 2 angles and the included sides (ASA) are given?
Take for instance a triangle with sides 5cm and 6cm and included angle 60 degrees. Can you find all other angles and sides?
mathmaniac is offline  
 
February 2nd, 2013, 04:47 PM   #2
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1039

Re: find the angles and sides of the triangle

You should know this!
http://www.ehow.com/how_8311180_calcula ... ngths.html
Denis is offline  
February 2nd, 2013, 06:29 PM   #3
Senior Member
 
Joined: Dec 2012

Posts: 450
Thanks: 0

Re: find the angles and sides of the triangle

Quote:
Originally Posted by Denis
Please demonstrate it.
mathmaniac is offline  
February 2nd, 2013, 07:06 PM   #4
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1039

Re: find the angles and sides of the triangle

Quote:
Originally Posted by mathmaniac
Take for instance a triangle with sides 5cm and 6cm and included angle 60 degrees.
Can you find all other angles and sides?
x = 3rd side
Law of Cosines:
x^2 = 5^2 + 6^2 - 2(5)(6)COS(60)

Then calculate one missing angle using Law of Sines; then 3rd angle by default.
Denis is offline  
February 2nd, 2013, 07:40 PM   #5
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,968
Thanks: 1152

Math Focus: Elementary mathematics and beyond
Re: find the angles and sides of the triangle

Case 1: SSS:

Let the triangle have sides a = 4, b = 5 and c = 6 units in length and corresponding angles A, B and C.

From the Law of Cosines*, we have 6² = 4² + 5² - 2(4)(5)cos(C), where C is the angle between a and b. C = arccos(-1/.

By the Law of Sines*, sin(C)/c = sin(A)/a, so A = arcsin(asin(C)/c) = arcsin(?63/12), where A is the angle opposite a. A similar method may be used to find B, where B is the angle opposite b.


Case 2: SAS:

Apply the Law of Cosines to find the length of the side opposite the known angle then use the Law of Sines to compute the remaining angles.


Case 3: ASA:

Use the fact that the three angles of a triangle sum to ? radians to find the third angle, then use the Law of Sines to compute the remaining sides.



*Law of Cosines: The law of cosines states that a² = b² + c² - 2bccos(?), where the angle ? is the angle between sides b and c.

Let ABC be a triangle with sides a, b and c and corresponding angles A, B and C Let A be the angle opposite a. Then a² = (b - ccos(A))² + (csin(A))² = b² - 2bccos(A) + c²cos²(A) + c²sin²(A) = b² - 2bccos(A) + c²(cos²(A) + sin²(A)) = b² + c² - 2bccos(A).
The result is the same for any choice of angle.


*Law of Sines: The Law of Sines states that for a triangle ABC with sides a, b and c, the ratios between angles and opposite sides are equal. That is, if A is the angle opposite a, B is the angle opposite b and C is the angle opposite c, then sin(A)/a = sin(B)/b = sin(C)/c.

Let ABC be a triangle with sides a, b and c and corresponding angles A, B and C. Construct an altitude h. Then bsin(A) = h = asin(B), so sin(A)/a = sin(B)/b. A similar method may be employed for C and c.
greg1313 is offline  
February 4th, 2013, 04:53 PM   #6
Senior Member
 
Joined: Dec 2012

Posts: 450
Thanks: 0

Re: find the angles and sides of the triangle

I do it differently;
For SSS
I don't know any law of cosines, I do it by calculating the area using heron's formula, then find the height and then find angles by calculating tan, sin or any other thing and try finding values of angles that give the closest value of tan or sin
For SAS
I find the sines or tans or any other thing of the angle and then find the the other side and then the remaining angles.
For ASA
I find the third angle, then find values of tan, sin.....of the angles and find the sides using them.

I think the first one is very different, but the other 2 are some sort of a general procedure of what I do, I think.

Any way, thank you very much. The laws of sines and cosines are new to me. Maybe these would become useful to me in the future.
mathmaniac is offline  
February 4th, 2013, 05:03 PM   #7
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1039

Re: find the angles and sides of the triangle

Whatever turns you on, buddy.
Law of Sines/Cosines much quicker and simpler.
Denis is offline  
February 4th, 2013, 05:13 PM   #8
Senior Member
 
Joined: Dec 2012

Posts: 450
Thanks: 0

Re: find the angles and sides of the triangle

Can you give a proof of those?
mathmaniac is offline  
February 4th, 2013, 07:18 PM   #9
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1039

Re: find the angles and sides of the triangle

Use google. Nobody wants to reinvent the wheel.
Denis is offline  
February 5th, 2013, 12:36 PM   #10
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,968
Thanks: 1152

Math Focus: Elementary mathematics and beyond
Re: find the angles and sides of the triangle

. . . or see the bottom of my previous post in this topic .
greg1313 is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
angles, find, sides, triangle



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
find the sides and angles of triangle adilgrt007 Algebra 9 August 22nd, 2013 10:25 AM
Find Remaining Angles and Sides of triangle Britwells Algebra 3 March 27th, 2013 01:31 PM
Find all the sides of this triangle. mathmaniac Algebra 18 March 4th, 2013 05:40 PM
Solving for sides and angles of a triangle. Andrew Ryan Algebra 4 July 16th, 2011 01:35 AM
Calculate side from angles and some other sides in triangle Nicsoft Algebra 2 January 13th, 2010 12:35 PM





Copyright © 2019 My Math Forum. All rights reserved.