Question

the measure of angle bac can be calculated using the equation \\(\sin^{-1}\left(\frac{3.1}{4.5}\
ight) \approx x\\).
image of a right triangle with right angle at c, side bc = 3.1 in, side ac = 4.5 in, angle at a is x (angle bac). not drawn to scale
what is the measure of angle bac? round to the nearest whole degree.
\\(\circ\\) \\(0^\circ\\)
\\(\circ\\) \\(1^\circ\\)
\\(\circ\\) \\(44^\circ\\)
\\(\circ\\) \\(48^\circ\\)

Explanation:

Step1: Calculate the fraction inside the arcsin

First, we need to compute the value of $\frac{3.1}{4.5}$. Let's do that division: $\frac{3.1}{4.5} \approx 0.6889$.

Step2: Compute the arcsin of the result

Now, we need to find the angle whose sine is approximately 0.6889. Using a calculator (in degree mode), we calculate $\sin^{-1}(0.6889)$. Let's perform this operation: $\sin^{-1}(0.6889) \approx 43.5^\circ$, which rounds to $44^\circ$.

Answer:

44° (corresponding to the option: 44°)