Answer :
To determine the measure of angle \( \angle BAC \) given the equation \( \cos^{-1}\left(\frac{3.4}{10}\right) = x \), we need to solve for \( x \) in degrees and round it to the nearest whole degree.
1. First, recognize that \( \cos^{-1} \) is the arccosine function, which gives the angle whose cosine is the given number.
2. Here, we have \( \cos^{-1}\left(\frac{3.4}{10}\right) \).
3. Simplify the fraction \(\frac{3.4}{10}\):
[tex]\[ \frac{3.4}{10} = 0.34 \][/tex]
4. Next, find the arccosine of \( 0.34 \). The arccosine function or \( \cos^{-1} \) for \( 0.34 \) will give us an angle in radians.
5. Convert the angle from radians to degrees since we seek the measure in degrees.
After calculating, the measure of \( \angle BAC \) is found to be \( 70^{\circ} \).
Thus, the degree measure of angle \( BAC \) rounded to the nearest whole degree is:
[tex]\[ 70^{\circ} \][/tex]
So the correct answer is:
[tex]\[ 70^{\circ} \][/tex]
1. First, recognize that \( \cos^{-1} \) is the arccosine function, which gives the angle whose cosine is the given number.
2. Here, we have \( \cos^{-1}\left(\frac{3.4}{10}\right) \).
3. Simplify the fraction \(\frac{3.4}{10}\):
[tex]\[ \frac{3.4}{10} = 0.34 \][/tex]
4. Next, find the arccosine of \( 0.34 \). The arccosine function or \( \cos^{-1} \) for \( 0.34 \) will give us an angle in radians.
5. Convert the angle from radians to degrees since we seek the measure in degrees.
After calculating, the measure of \( \angle BAC \) is found to be \( 70^{\circ} \).
Thus, the degree measure of angle \( BAC \) rounded to the nearest whole degree is:
[tex]\[ 70^{\circ} \][/tex]
So the correct answer is:
[tex]\[ 70^{\circ} \][/tex]
