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Find the missing side lengths. Answers should be simplified radicals (no decimals).

Find the missing side lengths. Answers should be simplified radicals (no decimals-example-1

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Given:

The right triangle is given.

Use the sin ratio to find the hypotenuse of the triangle.


\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}} \\ \sin 45^(\circ)=\frac{2\sqrt[]{2}}{b} \\ \frac{1}{\sqrt[]{2}}=\frac{2\sqrt[]{2}}{b} \\ b=4 \end{gathered}

Now, use the cosine ratio to find the remaining side of the triangle,


\begin{gathered} \cos \theta=\frac{adjecent\text{ side}}{\text{hypotenuse}} \\ \cos 45^(\circ)=(a)/(4) \\ \frac{1}{\sqrt[]{2}}=(a)/(4) \\ a=2\sqrt[]{2} \end{gathered}

Answer:


\begin{gathered} a=2\sqrt[]{2} \\ b=4 \end{gathered}

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