Question

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

Answer 1

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!