Question

find β in degrees.
12
7
β = ?°
round to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle $\beta$, the adjacent side $a = 12$ and the opposite side $o=7$. We use the tangent function: $\tan\beta=\frac{o}{a}$.
So, $\tan\beta=\frac{7}{12}$.

Step2: Solve for $\beta$

Take the inverse tangent (arctan) of both sides: $\beta=\arctan(\frac{7}{12})$.
Using a calculator, $\beta=\arctan(\frac{7}{12})\approx30.26^{\circ}$.

Answer:

$30.26$