Question

besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? round to the nearest degree. 18° and 39° 23° and 67° 43° and 47° 65° and 25°

Explanation:

Step1: Use trigonometric ratios

Let's assume the angles are \(A\) and \(B\). For angle \(A\) opposite to side \(5\), \(\sin A=\frac{5}{13}\).

Step2: Calculate angle \(A\)

\(A = \sin^{- 1}(\frac{5}{13})\approx23^{\circ}\) (using a calculator).

Step3: Calculate angle \(B\)

Since the sum of angles in a triangle is \(180^{\circ}\) and one angle is \(90^{\circ}\), \(B=90^{\circ}-A\). So \(B = 90^{\circ}-23^{\circ}=67^{\circ}\)

Answer:

23° and 67°