Question

If A is an obtuse angle in a triangle and sin A is 5/13, calculate the exact value of sin 2A

Answer 1

cos A = √( 1 - (5/13)²) = √( 1 - 25/169) = √(144/169) = - 12 /13 ( it is negative because A is an obtuse angle ).
sin 2 A = 2 sin A cos A
sin 2 A = 2 · 5/13 · ( - 12/13 ) = - 120 / 169