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Grade 9Magical Mathematics[Interesting Approach]

If the angle of triangles are in the ratio 2:3:7, then the sides are in ratio of?

PLS EXPLAIN!!!!!!

Profile image of Shivam Bhagat
14 Years agoGrade 9
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2 Answers

Profile image of shaswat roy
14 Years ago

the ratio of the angles are given, therefore by using the fact that sum of three angles  is 180 deg, you will get the 3 angles of the triangle which are 30deg,45deg,105deg. find the sine of these angles and then simply use sine rule.

Profile image of himanshu  panwar
14 Years ago

Let a,b,c be the sides and A,B,C be the angles of a triangle

Given  A:B:C =2:3:7

A=2x ; B=3x ; C=7x ;

A+B+C =180  or

2x+3x+7x =180 

then x=15

or

A=30° ; B=45° ; C=105° ;

By sine rule 

a:b:c = sineA : sineB : sineC

a:b:c = sine30 : sine45 : sine(60+45)

       =1/2 : 1/√2 : ( √3/2√2 + 1/2√2 )

 

hence a : b : c  =  √2 : 2 : (√3 + 1)