Question

15 a ramp is designed with the profile of a right triangle. the measure of one acute angle is 2 times the measur of the other acute angle. find the measure of the two acute angles. a ( 45^{circ}, 45^{circ} ) b ( 11.25^{circ}, 78.75^{circ} ) c ( 22.5^{circ}, 67.5^{circ} ) d ( 30^{circ}, 60^{circ} )

Explanation:

Step1: Let the measure of the smaller acute angle

Let the measure of the smaller acute angle be \(x\). Then the measure of the larger acute angle is \(2x\).

Step2: Use the property of angles in a right - triangle

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, \(x + 2x=90^{\circ}\).

Step3: Solve the equation

Combine like terms: \(3x = 90^{\circ}\). Then \(x=\frac{90^{\circ}}{3}=30^{\circ}\).

Step4: Find the measure of the other acute angle

If \(x = 30^{\circ}\), then \(2x=2\times30^{\circ}=60^{\circ}\).

Answer:

D. \(30^{\circ},60^{\circ}\)