Question

9.6
score: 8/15 answered: 8/15
question 9
in a right triangle, one of the acute angles is twice as large as the other acute angle. find the measure of the two acute angles.
the two acute angles are degrees.
question help: video message instructor

Explanation:

Step1: Set up the equation

Let one acute angle be \(x\) degrees. Then the other acute angle is \(2x\) degrees. In a right - triangle, the sum of the two acute angles is \(90^{\circ}\) (since the sum of angles in a triangle is \(180^{\circ}\) and one angle is \(90^{\circ}\)). So, \(x + 2x=90\).

Step2: Solve the equation

Combine like terms: \(3x = 90\). Divide both sides by 3: \(x=\frac{90}{3}=30\).

Step3: Find the second acute angle

If \(x = 30\), then \(2x=2\times30 = 60\).

Answer:

\(30\) and \(60\)