SOLUTION: Hello I'm given a Right Triangle EFG. EF being the hypotenuse with a altitude which is HG. Segment GF=20 and segment EF=25. The question is Find the length of HF. I just can't se

Algebra ->  Triangles -> SOLUTION: Hello I'm given a Right Triangle EFG. EF being the hypotenuse with a altitude which is HG. Segment GF=20 and segment EF=25. The question is Find the length of HF. I just can't se      Log On


   

Question 112539This question is from textbook
: Hello I'm given a Right Triangle EFG. EF being the hypotenuse with a altitude which is HG. Segment GF=20 and segment EF=25. The question is Find the length of HF.
I just can't seem to figure this one out I'm not having any trouble on any of the other ones. Well i hope my description is good enough, Thank You. This question is from textbook

Answer by ilana(307) About Me  (Show Source):
You can put this solution on YOUR website!
The trick to this is you need to realize that EFG and GFH are similar triangles. This is because the angle at F is shared by both and angles G and H are both right angles (an altitude meets the opposite side at a right angle). So the remaining angles, E and G, must be the same, too, to add to 180 degrees.
(You could also use the angle, side, angle method of seeing similar triangles)
With similar triangles, setting up a proportion helps you solve for the lengths. So GF/EF = HF/GF. Using the numbers we have, 20/25 = x/20. Cross multiply to get 25x=400, so x=16. That is the length of HF.