First, let's solve for [tex]\( x \)[/tex]:
[tex]\[ x = -\left(\frac{3.4}{10}\right) \][/tex]
Simplify the fraction:
[tex]\[ \frac{3.4}{10} = 0.34 \][/tex]
Apply the negative sign:
[tex]\[ x = -0.34 \][/tex]
Next, we need to determine the angle [tex]\( \angle BAC \)[/tex] whose cosine is [tex]\( -0.34 \)[/tex]. This involves using the inverse cosine (arccos) function:
[tex]\[ \angle BAC = \arccos(-0.34) \][/tex]
When we evaluate the inverse cosine of [tex]\( -0.34 \)[/tex], we find that:
[tex]\[ \arccos(-0.34) \approx 1.9177 \text{ radians} \][/tex]
To convert the value from radians to degrees, we use the conversion factor [tex]\( \frac{180}{\pi} \)[/tex]:
[tex]\[ \angle BAC = 1.9177 \times \frac{180}{\pi} \][/tex]
Approximating [tex]\( \pi \)[/tex] to 3.14159, we get:
[tex]\[ \angle BAC \approx 1.9177 \times 57.2958 \][/tex]
When we multiply these values together:
[tex]\[ \angle BAC \approx 109.8769^\circ \][/tex]
Finally, we round [tex]\( 109.8769^\circ \)[/tex] to the nearest whole degree:
[tex]\[ \angle BAC \approx 110^\circ \][/tex]
Thus, the degree measure of [tex]\( \angle BAC \)[/tex] is [tex]\( 110 \)[/tex] degrees. Given the provided answer choices, the angle [tex]\( \angle BAC \)[/tex] rounded to the nearest whole degree is:
[tex]\[ 70^{\circ} = false \][/tex]
[tex]\[ 71^{\circ} = false \][/tex]
[tex]\[ 19^{\circ} = false \][/tex]
[tex]\[ 20^{\circ} = false \][/tex]
But correct rounded answer is [tex]\(110 \text{ degrees} \)[/tex], but none of provided options matches the correct right one.
