In a right triangle if one acute angle has a measure of 10 x + 3 and the other has a measure of 3x + 9 find the larger of these two angles

QUESTION POSTED AT 01/06/2020 - 04:47 PM

Answered by admin AT 01/06/2020 - 04:47 PM

Hello,
Since we're given that both of these angles are acute(less than 90 degrees), we can form these 2 inequalities:10x+3\ \textless \ 90 and 3x+9\ \textless \ 90. Isolating x in both inequalities we get: x\ \textless \ 6.7 and x\ \textless \ 27. Therefore we have 6.7\ \textgreater \ x\ \textless \ 27. Now let's form another inequality byadding the 2 original inequalities: 10x+3+3x+9\ \textless \ 180. Simplifying we get 13x+12\ \textless \ 180. Solving for x we get x\ \textless \  14. So now we have 6.7\ \textgreater \ x\ \textless \ 14.Therefore, x must be positive and for any positive x in this range 10x+3 is greater than 3x+9. Let me know if that doesn't make sense!
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