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# Ruth is setting up the locations of the corners of a 10' by 24' rectangular deck she is going to build in her backyard. To make sure she has a perfect rectangle, she checks to make sure the diagonals are the same. a. What should the length of each diagonal be? b. What angle does the diagonal make with the longer side of the deck? Round to the nearest degree. c. What angle does the diagonal make with the shorter side of the deck? Round to the nearest degree.

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#### a.

Determine the length of the diagonal.

\begin{align*} a^{2} + b^{2} &= c^{2} && \text{Write the formula for Pythagorean theorem}\\ 24^{2} + 10^{2} &= c^{2} && \text{Substitute the values}\\ 576 + 100 &= c^{2} && \text{Evaluate the exponent}\\ 676 &= c^{2} && \text{Add the values}\\ \sqrt{676} &= \sqrt{c^{2}} && \text{Use square root to remove exponent}\\ 26 &= c && \text{Simplify} \end{align*}

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