A right triangle has a hypotenuse of length 99 inches. if one angle is 34 degrees34°, find the length of each leg.
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Assuming a diagram similar to the one I've attached, ∠<em>YVZ</em> is a vertical angle to ∠<em>WVX</em>, which means they have an equal measure. Additionally, ∠<em>WVZ</em> and ∠<em>WVX</em> form a linear pair, which means they are supplementary (sum to 180°). That means we start out with the equation
We combine our like terms (the <em>x</em>'s get combined, then the constants get combined) and have:
Cancel the 9 first by subtraction:
Cancel the 19 by division:
Since we know that our angle we're looking for, ∠<em>YVZ</em>, is the same measure as ∠<em>WVX</em>, we substitute 9 in for <em>x</em>:
8(9)+28=72+28=100°
We combine our like terms (the <em>x</em>'s get combined, then the constants get combined) and have:
Cancel the 9 first by subtraction:
Cancel the 19 by division:
Since we know that our angle we're looking for, ∠<em>YVZ</em>, is the same measure as ∠<em>WVX</em>, we substitute 9 in for <em>x</em>:
8(9)+28=72+28=100°