Let's determine in which triangle the value of [tex]\( x \)[/tex] equals [tex]\( \cos^{-1}\left(\frac{4.3}{6.7}\right) \)[/tex]. We will go through the steps to find the value of [tex]\( x \)[/tex] in degrees and identify the correct triangle.
1. Calculate the ratio:
[tex]\[
\text{ratio} = \frac{4.3}{6.7}
\][/tex]
This ratio is approximately 0.6417910447761194.
2. Find the inverse cosine (arc cosine) value:
[tex]\[
x = \cos^{-1}(0.6417910447761194)
\][/tex]
The result of this calculation is approximately 0.8739648401891128 radians.
3. Convert the result from radians to degrees:
We use the conversion factor where [tex]\( 1 \)[/tex] radian equals [tex]\( \frac{180}{\pi} \)[/tex] degrees.
[tex]\[
x \text{ in degrees} = 0.8739648401891128 \times \frac{180}{\pi}
\][/tex]
This conversion gives us approximately 50.07449678566164 degrees.
4. Conclusion:
The value of [tex]\( x \)[/tex] for the required triangle is approximately [tex]\( 50.07^\circ \)[/tex].
We now look at the given triangles and determine which one has an angle closest to [tex]\( 50.07^\circ \)[/tex]. The triangle that contains this angle is the one where [tex]\( x \)[/tex] is equal to [tex]\( \cos^{-1}\left(\frac{4.3}{6.7}\right) \)[/tex].
