Let FGHB a right triangle with right angle G and an altitude as shown find XYZ

Answer:Part 1) [tex]z=4\sqrt{2}\ units[/tex]Part 2) [tex]x=18\ units[/tex]Part 3) [tex]y=12\sqrt{2}\ units[/tex]Step-by-step explanation:step 1Find the value of zIn the smaller right triangle IFG of the figureApplying the Pythagoras Theorem[tex]6^{2}=2^{2}+z^{2}[/tex][tex]z^{2}=6^{2}-2^{2}[/tex][tex]z^{2}=32[/tex]  [tex]z=4\sqrt{2}\ units[/tex]step 2In the right triangle HFGApplying the Pythagoras Theorem[tex]x^{2}=y^{2}+6^{2}[/tex][tex]y^{2}=x^{2}-36[/tex] -----> equation Astep 3In the right triangle HIGApplying the Pythagoras Theorem[tex]y^{2}=z^{2}+(x-2)^{2}[/tex][tex]y^{2}=32+(x-2)^{2}[/tex] -----> equation Bstep 4equate equation A and equation B[tex]x^{2}-36=32+(x-2)^{2}\\x^{2}-36=32+x^{2}-4x+4\\4x=36+36\\4x=72\\x=18\ units[/tex]step 5Find the value of ySubstitute the value of x in the equation Bwe have[tex]x=18\ units[/tex][tex]y^{2}=32+(18-2)^{2}[/tex][tex]y^{2}=32+(16)^{2}[/tex][tex]y^{2}=288[/tex][tex]y=12\sqrt{2}\ units[/tex]