SOLUTION: In right Triangle ABC the altitude segment CH to the hypotenuse segment AB intersects angle bisector segment AL in point D. Find BC if AD=8cm and DH=4cm.
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Question 1103311: In right Triangle ABC the altitude segment CH to the hypotenuse segment AB intersects angle bisector segment AL in point D. Find BC if AD=8cm and DH=4cm. Answer by greenestamps(13216) (Show Source):
From the given information, we can see that triangle ADH is a right triangle with right angle at H, and with DH=4 and AD=8. That makes it a 30-60-90 right triangle, with AH=4*sqrt(3).
Since AL is the angle bisector, angle A is 60 degrees.
That means triangles AHC, CHB, and ACB are all 30-60-90 right triangles.
