The hypotenuse of a right triangle measures 10 units. One of its non-right angles measures. Find the measure of the side opposite of that angle. Round your answer to the nearest hundredth.

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The hypotenuse of a right triangle measures 10 units. One of its non-right angles measures<br><br><img src='https://www.fatskills.com/images2/GradExams/4E7BCFD4-0853-4DC9-9978-A9AB2EC7913D.png' height='15' width='27'/>. Find the measure of the side opposite of that angle. Round your answer to the nearest hundredth.