a carpenter uses a 12 foot timber to brace a wall frame 8 feet high. if the construction site is level what is the distance the timber will extend out from the wall frame ?

\(\text{Assuming the wall is plumb, the timber, the wall, and the ground form a right triangle}\\ \text{Using the pythagorean theorem and recognizing that the brace will be the hypotenuse we have}\\ \ell = \sqrt{12^2-8^2} = \sqrt{144-64} = \sqrt{80}=4\sqrt{5}~ft\)

\(\text{Assuming the wall is plumb, the timber, the wall, and the ground form a right triangle}\\ \text{Using the pythagorean theorem and recognizing that the brace will be the hypotenuse we have}\\ \ell = \sqrt{12^2-8^2} = \sqrt{144-64} = \sqrt{80}=4\sqrt{5}~ft\)