Question

solving for the unknown angle measures of a right triangle. 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 inverse - sine function

Let's find one of the non - right angles. We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. If we consider the angle opposite the side of length 5, $\sin\theta_1=\frac{5}{13}$. Then $\theta_1 = \sin^{- 1}(\frac{5}{13})$.
Using a calculator, $\theta_1=\sin^{-1}(\frac{5}{13})\approx23^{\circ}$.

Step2: Find the second non - right angle

Since the sum of the interior angles of a triangle is $180^{\circ}$ and one angle is $90^{\circ}$, and we found $\theta_1\approx23^{\circ}$, the second non - right angle $\theta_2=180^{\circ}-90^{\circ}-\theta_1$.
$\theta_2 = 90^{\circ}-\theta_1\approx90^{\circ}-23^{\circ}=67^{\circ}$.

Answer:

B. $23^{\circ}$ and $67^{\circ}$