My Math Forum  

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

Algebra Pre-Algebra and Basic Algebra Math Forum

LinkBack Thread Tools Display Modes
May 13th, 2013, 11:55 PM   #1
Joined: May 2013

Posts: 3
Thanks: 0

Triangle possibilities

Let x, y, ? be positive real numbers with ? < ? . We want to construct a triangle in which two sides have lengths x and y and one angle has measure ?. Up to congruence, how many such triangles are there? For each statement below, write whether it is TRUE or FALSE.
a) For some values of x, y, ? there is no such triangle.
b) For some values of x, y, ? there is exactly one such triangle.
c) For some values of x, y, ? there are exactly two such triangles.
d) For some values of x, y, ? there are exactly three such triangles

I get why a) is false but can somebody explain to me, or prove why b), c), d), are true?
ewler is offline  
May 14th, 2013, 07:11 AM   #2
Senior Member
Joined: Sep 2010

Posts: 221
Thanks: 20

Re: Triangle possibilities

With any given angle there are always two possibilities: if x>y the triangle is possible when
1) the angle is between x and y;
2) the angle is between y and the third side.
For definite values of x, y, and angle <90, all three possibilities exist.
So a) and b) are false; c) and d) are true.
McPogor is offline  
May 14th, 2013, 08:02 AM   #3
Global Moderator
Joined: Dec 2006

Posts: 18,034
Thanks: 1393

That analysis is incorrect.

(a) This is false, as a triangle exists with sides of length x and y, and the given angle in between them.

(b) This is true. If x = y and the given angle is ?/3, the triangle is equilateral.

(c) This is true. If x = 3, y = 4 and the angle is ?/2, the third side is either 5 or ?7.

(d) This is true. Example: x = 1 + ?3, y = ?2 and angle is ?/6.
skipjack is offline  

  My Math Forum > High School Math Forum > Algebra

possibilities, 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
Math Possibilities martapag Elementary Math 4 January 23rd, 2013 08:02 AM
Possibilities with thirteen numbers davidbenjamindix Advanced Statistics 1 January 7th, 2013 03:31 PM
Coin Purchase Possibilities testtrail429 Algebra 1 October 11th, 2012 12:57 AM
The possibilities of the dice of numbers 1 -3 (?) Keroro Algebra 4 June 5th, 2012 06:05 PM
Possibilities tuloon Algebra 1 April 9th, 2009 11:56 AM

Copyright © 2017 My Math Forum. All rights reserved.