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: Identify triangle type

It's a right triangle with sides 5, 12, and hypotenuse 13 (since \(5^2 + 12^2 = 25 + 144 = 169 = 13^2\)).

Step2: Calculate first angle

Let \( \theta_1 \) be the angle opposite side 5. Using \( \sin\theta_1 = \frac{5}{13} \), \( \theta_1 = \arcsin(\frac{5}{13}) \approx 22.6^\circ \approx 23^\circ \).

Step3: Calculate second angle

The other acute angle \( \theta_2 = 90^\circ - 23^\circ = 67^\circ \) (since angles in a triangle sum to \(180^\circ\), and one is \(90^\circ\)).

Answer:

23° and 67° (the option with 23° and 67°)