In right △ABC, m∠B = 30°. Also, AB = 14 3 and AD bisects ∠BAC. Find BD

Question

In right △ABC, m∠B = 30°. Also, AB = 143

 and AD bisects ∠BAC.

Find BD.

Answer 1

m<BAC = 60 (180 - right angle C and 30 degree angle B)

Since AD bisects <BAC, m<BAD and m<DAC = 30.

m<ADC = 180 - m<DAC - right angle C = 60.

AC is opposite 30 degree angle so equals 1/2 of AB = 7sqrt(3)

BC is opposite 60 degree angle BAC, so equal 7*sqrt(3)*sqrt(3) = 21

In triangle ADC, AC is opposite 60 degree angle, and DC is opposite 30 degree angle to DC = AC/sqrt(3) = 7.

BD = BC - DC = 21 - 7 = 14.