In triangle ABC angle B=30, AB= 4 in, BC=6 in, BL is an angle bisect or. What is the area of ABL?

Answer 1

need trigonometry for this solution

area ABC=(1/2)(4)(6)sin(30)=6

area ABL+area CBL=area ABC

area ABL+area CBL=(1/2)(4)(BL)sin(15)+(1/2)(6)(BL)sin(15)

BL=(12/10)(1/sin(15))

area ABL=(1/2)(4)(12/10)(1/sin(15))sin(15)=2.4 square in.