+45 In triangle ABC, point D lies on side AC such that line segment BD bisects angle ABC. Angle A measures 30 degrees, angle C measures 90 degrees, and the length of side AC is 12 units. The task is to determine the area of triangle ABD.
+129895 A 30
12 D
C 90 B
Angle B = 60
So angle BCD = 30
Side BC = 12/sqrt 3 = 4sqrt 3
So...in triangle BDC,, DC = BC / sqrt 3 = 4sqrt 3 /sqrt 3 = 4
Area of BDC = (1/2) BC * DC = (1/2) (4sqrt 3) (4) = 8 sqrt 3
Area of ABC = (1/2) (AC)(BC) = (1/2)(12)(4sqrt 3) = 24sqrt 3
So.... [ ABD ] = [ ABC ] - [ BDC ] = 24sqrt 3 - 8sqrt 3 = 16 sqrt 3
CORRECTED
