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!