The altitude to the hypotenuse of a right triangle ABC divides the hypotenuse into 12mm and 16mm segments. Find the lengths of each of the following. A. The altitude to the hypotenuse B. The shorter leg of angle ABC C. The longer leg of angle ABC
Added by Jamie P.
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We know that the altitude to the hypotenuse divides the hypotenuse into 12mm and 16mm segments. Let's label the altitude as h, the shorter leg as a, and the longer leg as b. [Insert image of triangle ABC with labels] Show more…
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The altitude, $\overline{C D}$ , to the hypotenuse, $\overline{A B}$ , of right triangle $A B C$ separates the hypotenuse into two segments, $\overline{A D}$ and $\overline{D B}$ . If $A D=D B+4$ and $C D=12$ centimeters, find $D B, A D,$ and $A B$ . Recall that the length of the altitude to the hypotenuse of a right triangle is the mean proportional between the lengths of the segments into which the hypotenuse is separated, that is, $\frac{A D}{C D}=\frac{C D}{D B}$
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