To find the measure of the angle [tex]\(\theta\)[/tex] given the equation [tex]\(\theta = \sin^{-1}\left(\frac{16}{25}\right)\)[/tex], follow these steps:
1. Understand the equation: The equation [tex]\(\theta = \sin^{-1}\left(\frac{16}{25}\right)\)[/tex] tells us that we are looking for the angle [tex]\(\theta\)[/tex] whose sine is [tex]\(\frac{16}{25}\)[/tex].
2. Compute [tex]\(\sin^{-1}\left(\frac{16}{25}\right)\)[/tex]: To find this angle, we use the inverse sine function (also called the arcsine function). The arcsine function [tex]\(\sin^{-1}(x)\)[/tex] returns the angle whose sine is [tex]\(x\)[/tex].
3. Find the angle: We know from the provided data that if [tex]\(\sin^{-1}\left(\frac{16}{25}\right)\)[/tex], the result is approximately 39.791819499557235 degrees.
4. Round to the nearest tenth: The number 39.791819499557235 rounded to the nearest tenth is 39.8.
So, the measure of the angle [tex]\(\theta\)[/tex] is approximately [tex]\(39.8^\circ\)[/tex]. Therefore, the correct answer is:
b. [tex]\(39.8^\circ\)[/tex]
