Geometry!!

Question

In right triangle FGH shown below, m∠GHF  90, altitude is drawn to , FJ  16, and HG  15.

 

Find the length of JG and HJ.

 

(This won't let me draw the picture but there are no corresponding lengths of any of the similar triangles. The lengths 15 and 16 don't correspond to each other and the only other right angles are located at /FJH and /GJH)  

 

HELP!!!!!?????

 

Answer 1

Maybe this rough diagram would help sort things out.  Let us know whether it is equivalent to what you're seeing.

 

I'm guessing the figure looks something very similar to (equivalent) to the sketch below.

               H

               ^  <- right angle

     15 /    |           \            x

       /    b |                       \

    /_ _ _  |90_  _  _  _  _  _  _  _\
G       a    J              16                  F

 

**If I've misinterpreted this, the values for any final answers aren't going to matter, but try using the similar triangle approach and remember that you aren't always going to get values that are integers in the end!**

 

I'm thinking this is likely to match your example, since I get a = 9 and b = 12.  A hint I like to share with my students is that it is pretty common to get some version (a multiple) of a 3-4-5 Right Triangle (or a 5-12-13 Right Triangle) when given an example to work out from a textbook.  The 15 is the figure that gave me a clue since it is 3 time 5 and that side was the hypotenuse for the right triangle HJG.

Answer 2

Look at the three different right triangles once you draw point J on segment GF.

 

You are going to have some similar triangles using angles.

 

I am on the run, I will finish the problem as soon as I can.

 

Sorry??????????????