Question 1116027: In ΔABC, m∠A = 90° and AN is an altitude. If AB = 20 in and AC = 15 in, find BC, BN, NC, AN.
I know that BC = 25 because of the 3,4,5 triple but that's all I can figure out.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39613)   (Show Source):
You can put this solution on YOUR website! Draw the figure. Label the parts. You correctly found that BC is 25 inches.
Now you have two right triangles which share a side AN.
If CN is x, then BN is 25-x. You could use Pythagorean Theorem formula again, for both triangles.
Let altitude AN be h for "height". Length AN is h.
If this makes sense to you, then you can solve for h and x.
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(Can you find a theorem about triangles which gives information about this kind of description?)
Answer by greenestamps(13195)  (Show Source):
You can put this solution on YOUR website!
The altitude AN to hypotenuse BC creates two right triangles, NBA and NAC, that are both similar to triangle ABC.
Use the 25 length of BC that you found to set up proportions between corresponding sides of the right triangles. For example, comparing short side to hypotenuse in triangles NBA and ABC gives
From there the rest of the problem is easy.
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