Question

find α in degrees.
α = ?°
round to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle $\alpha$ is defined as $\cos\alpha=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side to angle $\alpha$ is $6$ and the hypotenuse is $10$. So, $\cos\alpha=\frac{6}{10}=0.6$.

Step2: Find the angle using the inverse cosine function

We know that if $\cos\alpha = x$, then $\alpha=\cos^{-1}(x)$. So, $\alpha=\cos^{-1}(0.6)$.
Using a calculator, $\cos^{-1}(0.6)\approx53.13^{\circ}$ (rounded to the nearest hundredth).

Answer:

$53.13$