Question

for angle measures of right triangles
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?
59.0°
53.1°
36.9°
31.0°

Explanation:

Step1: Recall cosine - ratio in right - triangle

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

Step2: Substitute given values

We know that \(AC = 25\) cm and \(BC = 15\) cm. So, \(\cos(\angle ACB)=\frac{15}{25}=\frac{3}{5}=0.6\).

Step3: Find the angle

We need to find \(\angle ACB\) such that \(\cos(\angle ACB)=0.6\). Using the inverse - cosine function, \(\angle ACB=\cos^{-1}(0.6)\).
\(\angle ACB\approx53.1^{\circ}\)

Answer:

53.1°