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: Recall cosine - ratio formula

In right - triangle \(ABC\) with right - angle at \(B\), \(\cos\angle ACB=\frac{BC}{AC}\).

Step2: Substitute given values

Given \(AC = 25\) cm and \(BC = 15\) cm, then \(\cos\angle ACB=\frac{15}{25}=\frac{3}{5}=0.6\).

Step3: Find the angle

\(\angle ACB=\cos^{- 1}(0.6)\approx53.1^{\circ}\) (using a calculator to find the inverse - cosine of \(0.6\)).

Answer:

C. \(53.1^{\circ}\)