To solve this problem, we need to follow a few steps.
1. Understanding the fraction:
The question gives us the fraction [tex]\(\frac{5}{8.3}\)[/tex].
2. Calculating the value of the fraction:
We start by simplifying the fraction:
[tex]\[
\frac{5}{8.3} \approx 0.6024
\][/tex]
3. Finding the angle whose sine is the given fraction:
We need to find the angle [tex]\( x \)[/tex] such that
[tex]\[
\sin(x) = 0.6024
\][/tex]
To obtain this angle, we use the inverse sine function, also known as [tex]\(\sin^{-1}\)[/tex] or [tex]\(\arcsin\)[/tex].
4. Calculating the angle in radians:
Using [tex]\(\arcsin\)[/tex] on the value [tex]\(0.6024\)[/tex], we get:
[tex]\[
x = \arcsin(0.6024) \approx 0.6465 \text{ radians}
\][/tex]
5. Converting the angle from radians to degrees:
Since many geometric problems prefer degrees, we convert radians to degrees using the conversion factor [tex]\(\frac{180}{\pi}\)[/tex]. Thus,
[tex]\[
x \approx 0.6465 \times \frac{180}{\pi} \approx 37.04 \text{ degrees}
\][/tex]
Therefore, the measure of the unknown angle [tex]\( x \)[/tex] in a triangle is approximately 37.04 degrees, as it equals [tex]\(\sin^{-1}\left(\frac{5}{8.3}\right)\)[/tex].
