Question

instructions
choose the best answer. if necessary, use the paper you were given.
question
note: figure not drawn to scale.
in the right triangle above, ( b > a ). which of the following could be the value of ( x )?
95
72
45
36

Explanation:

Step1: Recall triangle angle sum property

In a right - triangle, the sum of angles is \(180^{\circ}\). One angle is \(90^{\circ}\), so \(x + y=90\), and \(y = 90 - x\).

Step2: Use side - angle relationship

In a triangle, the larger side is opposite the larger angle. Given \(b > a\), so \(y>x\) (since side \(b\) is opposite angle \(y\) and side \(a\) is opposite angle \(x\)). Substituting \(y = 90 - x\) into \(y>x\), we get \(90 - x>x\).

Step3: Solve the inequality

\(90 - x>x\)
\(90>2x\)
\(x < 45\)

Answer:

36