37. In a triangle ABC, a = 2 + 13, ...
Question

# 37. In a triangle ABC, a = 2 + 13, 2C = 60° then in the triangle (1) One angle is 105° (2) One angle is four times another angle (3) One angle is 25° (4) One angle is five times another angle AD

JEE/Engineering Exams
Maths
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( frac{sin A}{sin (A+60)}=frac{2+sqrt{3}}{1}, ) recognize the right hand side as tan ( 75 . ) So, using sine supplementary angle identiity ( sin theta=sin (180-theta) ) : [ frac{sin A}{sin (A+60)}=frac{sin 75}{cos 75}=frac{sin 75}{sin 15} ] ( quad=frac{sin 105}{sin 165}=frac{sin (105)}{sin (105+60)} ) Comparing arguments of first and last fractions we straightaway note that ( A=105 ) [ (A, B, C)=(105,15,60) ]