To find the measure of the unknown angle, [tex]\( x \)[/tex], in a triangle such that [tex]\( x = \sin^{-1}\left(\frac{5}{8.3}\right) \)[/tex], follow these steps:
1. Compute the ratio:
[tex]\[
\frac{5}{8.3} \approx 0.6024
\][/tex]
2. Calculate the angle in radians:
Using the inverse sine function, find the measure of the angle whose sine is 0.6024.
[tex]\[
x \approx \sin^{-1}(0.6024) \approx 0.6465 \text{ radians}
\][/tex]
3. Convert the angle from radians to degrees:
Since angles are often more conveniently expressed in degrees, convert the radians to degrees using the relation [tex]\(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\)[/tex].
[tex]\[
x \approx 0.6465 \text{ radians} \times \frac{180}{\pi} \approx 37.043 \text{ degrees}
\][/tex]
Therefore, in the triangle in question, the measure of the unknown angle [tex]\( x \)[/tex] is approximately [tex]\( 37.043 \)[/tex] degrees.
