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 function in right - triangle

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

Step2: Substitute given values

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

Step3: Find the angle

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

Answer:

$53.1^{\circ}$