A13foot lader i upagenst a tree the bottom of the ladder is 5 feet away form the tree how high is the ladder on the tree

Think of the 13-ft length of the ladder as the hypotenuse of a right triangle. Represent the horiz. distance from foot of ladder to base of tree by x, or 5 ft.

Represent the vert. dist. from base of tree to top of ladder by y, which is unknown.

Then (13 ft)^2 = (5 ft)^2 + y^2, or

169 ft^2 = 25 ft^2 + y^2. This simplifies to y^2 = 144. Thus y = + 12 feeet.

Note: Please pay attention to your spelling: "lader i up agenst a tree" should be "the top of a 13-ft ladder is placed against a tree."

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