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 trigonometric ratio

In right triangle \(ABC\), \(\cos(\angle ACB)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{BC}{AC}\). Given \(BC = 15\) cm and \(AC=25\) cm.

Step2: Calculate cosine value

\(\cos(\angle ACB)=\frac{15}{25}=\frac{3}{5} = 0.6\)

Step3: Find angle measure

Using inverse cosine function, \(\angle ACB=\cos^{-1}(0.6)\). Calculating this, we get approximately \(53.1^{\circ}\)

Answer:

\(53.1^{\circ}\) (the option with \(53.1^{\circ}\))