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 the cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For angle \(ACB\) in right - triangle \(ABC\), the adjacent side to angle \(ACB\) is \(BC\) and the hypotenuse is \(AC\).

Step2: Substitute the values into the cosine formula

Let \(\theta = \angle ACB\), \(BC = 15\) (adjacent) and \(AC = 25\) (hypotenuse). Then \(\cos\theta=\frac{BC}{AC}\). Substituting the values, we get \(\cos\theta=\frac{15}{25}=0.6\).

Step3: Find the angle using the inverse cosine function

We know that \(\theta=\cos^{- 1}(0.6)\). Using a calculator, \(\cos^{-1}(0.6)\approx53.1^{\circ}\).

Answer:

\(53.1^{\circ}\)