Thread: 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>>

Hello anshulbshah

Originally Posted by anshulbshah

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 . Then the largest angle is . Since the triangle is acute-angled, , since must be an integer, and therefore a multiple of . This gives us that .

Next suppose that the third (middle-sized) angle of the triangle is . Using the angle-sum of a triangle, . The smallest possible value of is when is as large as possible; i.e. , and at this value the largest angle is .

If we make a bit smaller, say , then . But in this case , which is smaller than .

So the only solution is .

Grandad