Question 1129315
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(1) In right triangle AHD, leg HD is 4 and hypotenuse AD is 8.  That means AHD is a 30-60-90 right triangle.  That makes AH = 4*sqrt(3)<br>
(2) Since AL is the angle bisector of angle A and angle HAD is 30 degrees, angle A is 60 degrees.<br>
(3) Because angle A is 60 degrees, AHC and ABC are both 30-60-90 right triangles.<br>
(4) Since AHC is a 30-60-90 right triangle and AH = 4*sqrt(3), AC = 8*sqrt(3).<br>
(5) Since ABC is a 30-60-90 right triangle and AC = 8*sqrt(3), BC = (8*sqrt(3))*sqrt(3) = 24.<br>
ANSWER:  BC = 24