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 adjacent side/hypotenuse

For $\angle ACB$, adjacent side $BC = 15$ cm, hypotenuse $AC = 25$ cm.

Step2: Use cosine function definition

$\cos(\angle ACB) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{15}{25} = 0.6$

Step3: Calculate inverse cosine

$\angle ACB = \cos^{-1}(0.6)$
Using a calculator, $\cos^{-1}(0.6) \approx 53.1^\circ$

Answer:

53.1°