Question 1129315: In right △ABC the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find BC if AD = 8 cm and DH = 4 cm.
Answer by greenestamps(13200)   (Show Source):
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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)
(2) Since AL is the angle bisector of angle A and angle HAD is 30 degrees, angle A is 60 degrees.
(3) Because angle A is 60 degrees, AHC and ABC are both 30-60-90 right triangles.
(4) Since AHC is a 30-60-90 right triangle and AH = 4*sqrt(3), AC = 8*sqrt(3).
(5) Since ABC is a 30-60-90 right triangle and AC = 8*sqrt(3), BC = (8*sqrt(3))*sqrt(3) = 24.
ANSWER: BC = 24
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