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
August 15th, 2013, 05:48 AM   #1
Newbie
 
Joined: Aug 2013

Posts: 3
Thanks: 0

find the sides and angles of triangle

My question relating to trigonometry. A triangle having altitude magnitude is 40 and its base 100 and base opposite angle is 110 degree, so find the rest of all sides and angles. I attach picture that I draw rough sketch on paint so sorry about sketch. It will clear you the question... please answer my question as quickly as possible.
Attached Images
File Type: jpg a triangle having alltitude.jpg (25.0 KB, 226 views)
adilgrt007 is offline  
 
August 15th, 2013, 07:24 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 21,030
Thanks: 2260

When the altitude bisects the base, the angle at B is maximized, and would then be 2arctan(50/40), which is only about 102.68°, so the problem has no solution.
skipjack is online now  
August 15th, 2013, 11:42 AM   #3
Newbie
 
Joined: Aug 2013

Posts: 3
Thanks: 0

Re: find the sides and angles of triangle

@ skipjack why you take 50 for which method and principle?
adilgrt007 is offline  
August 15th, 2013, 02:26 PM   #4
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1039

Re: find the sides and angles of triangle

Is angle A = angle C? Your diagram seems to indicate so.
Denis is offline  
August 15th, 2013, 02:39 PM   #5
Member
 
Joined: Aug 2013

Posts: 59
Thanks: 0

If we call the base point D, then is ?ADB = ?CDB = 90° true?
slipjack is offline  
August 16th, 2013, 02:46 AM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 21,030
Thanks: 2260

I used 100/2 = 50 because I was considering the case where the altitude bisects the base. Using 50 - x and 50 + x, one would get arctan((50 - x)/40) + arctan((50 + x)/40) = 110°, which has no solution. The LHS is an even function and its maximum value occurs at x = 0.
skipjack is online now  
August 16th, 2013, 03:30 AM   #7
Senior Member
 
mrtwhs's Avatar
 
Joined: Feb 2010

Posts: 714
Thanks: 151

Re: find the sides and angles of triangle

Even if you don't assume that the altitude hits at the midpoint, there is no solution.

Suppose that the altitude divides the side of 100 into two parts ... x on the left and 100-x on the right. You then get



This simplifies to



which has a negative discriminant and thus has no real solutions.
mrtwhs is offline  
August 17th, 2013, 04:26 AM   #8
Newbie
 
Joined: Aug 2013

Posts: 3
Thanks: 0

Re: find the sides and angles of triangle

It's not a midpoint.
adilgrt007 is offline  
August 17th, 2013, 06:17 AM   #9
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1039

Re: find the sides and angles of triangle

Quote:
Originally Posted by adilgrt007
It's not a midpoint.
Well then, with height 40 and base 100, angle B = 110 degrees is impossible; did you guess?

Highest possible is ~103 degrees; that's with height line dividing AC in 49:51 ratio.
Denis is offline  
August 22nd, 2013, 10:25 AM   #10
Newbie
 
Joined: Jun 2013

Posts: 8
Thanks: 0

Re: find the sides and angles of triangle

You can apply the Generalized Pythagorean Theorem, let’s say that the foot of altitude is H so we have, note BH with x and HC with 100 – x so we have a equation in x with two solutions, both are valid.
constantin is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
angles, find, sides, triangle



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
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
find the angles and sides of the triangle mathmaniac Algebra 16 February 14th, 2013 06:27 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.