Question

find the measures of the angles of a right triangle where one of the acute angles is *3.5* times the other

Answer 1

Lets draw a picture of our problem:

where x denotes the measure of the base angle.

Since interior angles of any triangle add up to 180, we have

`x+3.5x+90=180`

which gives

`4.5x+90=180`

By subtracting 90 to both sides, we have

`\begin{gathered} 4.5x=180-90 \\ 4.5x=90 \end{gathered}`

Finally, by dividing both sides by 4.5, we get

`\begin{gathered} x=(90)/(4.5) \\ x=20 \end{gathered}`

Then, the base angle measures 20 degrees and the upper angle measure

`3.5*20=70`

Therefore, the searched angles measure

`20,70\text{ and 90}`