Sure! Let's look at the given equation:
[tex]\[
\cos^{-1}\left(\frac{3.4}{10}\right) = x
\][/tex]
We'll follow these steps to find the measure of angle BAC.
### Step 1: Calculate the Ratio
First, we need to calculate the ratio [tex]\(\frac{3.4}{10}\)[/tex]:
[tex]\[
\frac{3.4}{10} = 0.34
\][/tex]
This ratio is directly obtained as:
[tex]\[
0.34
\][/tex]
### Step 2: Find the Angle Using Inverse Cosine
Next, we need to find the angle [tex]\( x \)[/tex] in radians by calculating the inverse cosine (or arccos) of [tex]\( 0.34 \)[/tex]:
[tex]\[
x = \cos^{-1}(0.34)
\][/tex]
From the calculations, this gives us:
[tex]\[
x \approx 1.2238794292677349 \text{ radians}
\][/tex]
### Step 3: Convert Radians to Degrees (Optional)
If we want the angle in degrees, we need to convert the radians to degrees. The formula to convert radians to degrees is:
[tex]\[
\text{degrees} = x \times \frac{180}{\pi}
\][/tex]
Applying this conversion:
[tex]\[
1.2238794292677349 \text{ radians} \times \frac{180}{\pi} \approx 70.12312592992117 \text{ degrees}
\][/tex]
### Summary
We have calculated the following:
- The ratio [tex]\(\frac{3.4}{10} = 0.34\)[/tex]
- The angle [tex]\( x \)[/tex], which is [tex]\( \cos^{-1}(0.34) \approx 1.2238794292677349 \text{ radians} \)[/tex]
- The angle in degrees (optional), which is approximately [tex]\( 70.12312592992117 \text{ degrees} \)[/tex]
Hence, the measure of angle BAC is approximately [tex]\(1.2238794292677349\)[/tex] radians or [tex]\(70.12312592992117\)[/tex] degrees.
