If the sides of a triangle are in the ratio 2: root 6: (root 3)+1 , then the largest angle of the triangle will be? Ans is 75 deg

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Please find below the solution to the asked query:

As sides are in the ratio 2:6:3+1Let a=2 units ,b=6 units and c=3+1 units2<6<3+1Hence c is the greatest side.Now greatest angle is opposite to greatest side. By Cosine rule, we have,cosC=a2+b2-2ab2ab=22+62-3+122.2.6=4+6-3+1+2346=10-4-2346=6-2346Dividing each term by 23 we get,cos C=3-122=322-122=3212-1212=cos 30°.cos 45°-sin 30°.sin 45°Using identity cosA+B=cos A.cos B-sin A.sin B, we get,cos C=cos30°+45°=cos75°C=75°Hence greatest angle is 75°. Answer

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