Answer:
It's A . 13 / (5√10)
Step-by-step explanation:
AD = √(3^2 + 4^2) = √25
= 5 ( By the Pythagoras Theorem).
So sin 2α = 3/5 and cos 2α = 4/5.
m < B = α ( external angle of a triangle theorem)
and BD = AD = 5 (Isosceles triangle) and BC = 4+5 = 9.
AB = √(3^2 + 9^2) = √90 = 3√10
So sin α = 3 / 3√10 = = 1 /√10 and cos α = 9 /3√10 = 3/√10.
Finally sin 3α = sin (2α + α) = sin 2α cos α + cos 2α sin α
= 3/5 * 3 / √10 + 4/5 * 1/√10
= 13/(5√10).
