Question

MEDAL AND FANS PLZZZZ I NEED TO RAISE MY MATH GRADE RIGHT NOW IM AT A D
What is the length of stack C G with bar on top when AG = 15 in., AD = 9 in., and DC = 10 in.? Round your answer to the nearest tenth of an inch.

Answer 1

I am really bad at pothagorean theorem

Answer 2

Triangle ADG is a right triangle, so \[AD ^{2}+DG ^{2}=AG ^{2}\]
This is \[9^{2}+DG ^{2}=15^{2}\]
so \[DG=\sqrt{15^{2}-9^{2}}=\sqrt{225-81}=\sqrt{144}=12\]
Now...
Triangle CDG is also a right triangle, so \[CD ^{2}+CG ^{2}=DG ^{2}\]
which yields: \[10^{2}+CG ^{2}=12^{2}\]
CG=\[\sqrt{12^{2}-10^{2}}=\sqrt{144-100}=\sqrt{44}\approx6.7\]