Find the lenght of the bisector of angle C?

given a triangle ABC whose angles are A=40 degree, B=95 degree and side b=30cm. Find the lenght of the bisector of angle C?

Find the lenght of the bisector of angle C?
geometry blows
Reply:In triangle ABC





m%26lt;A = 40





m%26lt;B = 95





m%26lt;C = 180 -(95+40) = 45





let CD bisects angle C





in triangle ACD





A = 40 deg





ACD = 45/2 = 22.5





ADC = 180-(40+22.5) = 180 -62.5 = 117.5 deg





apply sine rule to triangle ACD





a/sinA = b/sinB = c/SinC





AC/sin ADC = CD/sin A





b/sin 117.5 = CD/sin40





but b = 30





30/sin117.5 = CD/sin40





CD = 30(sin 40/sin 117.5)





30(0.6427)/0.8870





= 21.74 cm





The length of angle bisector C is 21.74 cm