Results 1 to 2 of 2

Math Help - Finding the measure of angles...

  1. #1
    Junior Member
    Joined
    Sep 2009
    From
    Vadodara,Gujarat,India
    Posts
    33

    Question Finding the measure of angles...

    For an acute angled triangle,all its angles have measure in integral degree.The smallest angle has a mesure 1/5th the measure of largest.Find all the measures of triangle>>
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello anshulbshah
    Quote Originally Posted by anshulbshah View Post
    For an acute angled triangle,all its angles have measure in integral degree.The smallest angle has a mesure 1/5th the measure of largest.Find all the measures of triangle>>
    You can't solve problems like this by simple algebra - you have to use a little bit of 'trial and error'.

    First, let's suppose the smallest angle is x^o. Then the largest angle is 5x. Since the triangle is acute-angled, 5x < 90\Rightarrow 5x \le 85, since x must be an integer, and 5x therefore a multiple of 5. This gives us that 0<x\le 17.

    Next suppose that the third (middle-sized) angle of the triangle is y^o. Using the angle-sum of a triangle, y = 180 - 6x. The smallest possible value of y is when x is as large as possible; i.e. x = 17\Rightarrow y = 180 - 102 = 78, and at this value the largest angle is 5x=85^o.

    If we make x a bit smaller, say x = 16, then y = 180 - 96 = 84. But in this case 5x = 80, which is smaller than y.

    So the only solution is 17^o,78^o,85^o.

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Angles and the measure?
    Posted in the Geometry Forum
    Replies: 3
    Last Post: May 30th 2010, 07:12 AM
  2. Measure-angles
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: August 16th 2009, 06:04 AM
  3. Finding the measure of angles in a circleeeee
    Posted in the Geometry Forum
    Replies: 5
    Last Post: June 17th 2008, 07:50 AM
  4. Finding the measure of angles
    Posted in the Geometry Forum
    Replies: 11
    Last Post: September 19th 2007, 07:01 PM
  5. Replies: 3
    Last Post: July 10th 2007, 01:40 PM

Search Tags


/mathhelpforum @mathhelpforum