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? 53.1° 36.9° 59.0° 31.0°

Explanation:

Step1: Identify the sides relative to angle ACB

In right triangle \(ABC\), angle \(C\) is the right angle? Wait, no, angle \(ACB\) is at \(C\), so \(BC\) is adjacent to angle \(ACB\), \(AC\) is the hypotenuse. So we can use cosine: \(\cos(\angle ACB)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{BC}{AC}\)
\(\cos(\angle ACB)=\frac{15}{25}=\frac{3}{5} = 0.6\)

Step2: Find the angle whose cosine is 0.6

We use the inverse cosine function: \(\angle ACB=\cos^{-1}(0.6)\)
Calculating this, \(\cos^{-1}(0.6)\approx53.1^\circ\)

Answer:

\(53.1^\circ\)