Question

the length of the hypotenuse, line segment ac, in right triangle abc is 25 cm. the length of line segment bc is 15 cm. which is the approximate measure of angle acb? 31.0° 36.9° 53.1° 59.0°

Explanation:

Step1: Identify triangle parts

In right triangle \(ABC\), hypotenuse \(AC = 25\) cm, \(BC = 15\) cm. Let \(\angle ACB=\theta\). We use cosine: \(\cos\theta=\frac{BC}{AC}\).

Step2: Calculate cosine value

Substitute values: \(\cos\theta=\frac{15}{25}=0.6\).

Step3: Find angle

\(\theta=\arccos(0.6)\approx53.1^\circ\).

Answer:

53.1° (corresponding to the option with 53.1°)