To determine the measure of angle BAC, given the equation [tex]\(\cos^{-1}\left(\frac{3.4}{10}\right) = x\)[/tex], we'll follow these steps:
1. Understand the Equation: The equation [tex]\(\cos^{-1}\left(\frac{3.4}{10}\right) = x\)[/tex] tells us that [tex]\(x\)[/tex] is the angle whose cosine is [tex]\(\frac{3.4}{10}\)[/tex].
2. Calculate the Value of [tex]\(\frac{3.4}{10}\)[/tex]:
[tex]\[
\frac{3.4}{10} = 0.34
\][/tex]
3. Determine the Inverse Cosine (Arccos) of 0.34:
Using the inverse cosine function [tex]\(\cos^{-1}\)[/tex], we find the angle [tex]\(x\)[/tex] in radians:
[tex]\[
x = \cos^{-1}(0.34)
\][/tex]
4. Convert Radians to Degrees:
To convert the angle from radians to degrees, use the formula:
[tex]\[
\text{degrees} = x \times \frac{180}{\pi}
\][/tex]
5. Round the Result to the Nearest Whole Degree:
Performing these calculations, we find that the degree measure of angle BAC rounds to:
[tex]\[
70^{\circ}
\][/tex]
Therefore, the degree measure of angle BAC is [tex]\( \boxed{70^\circ} \)[/tex].
