Question

problem 12: (first taught in lesson 30) find the measures of the angles of a right triangle where one of the two acute angles measures 8 times the other. after you enter your answer press go.

Explanation:

Step1: Let the smaller acute angle be \(x\)

Since one acute angle is 8 times the other, the larger acute angle is \(8x\). In a right - triangle, the sum of the two acute angles is \(90^{\circ}\) (because the sum of angles in a triangle is \(180^{\circ}\) and the right angle is \(90^{\circ}\)). So, we have the equation \(x + 8x=90\).

Step2: Solve the equation

Combine like terms: \(9x = 90\). Then, divide both sides by 9: \(x=\frac{90}{9}=10\).

Step3: Find the other acute angle

The larger acute angle is \(8x\). Substitute \(x = 10\) into \(8x\), we get \(8\times10 = 80\).

Answer:

\(10^{\circ},80^{\circ},90^{\circ}\)