To solve for [tex]\(x\)[/tex] where [tex]\(x = \cos^{-1}\left(\frac{4.3}{6.7}\right)\)[/tex], we need to understand the relationship between the sides and the angle in a right triangle.
Given:
[tex]\[ \cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}} \][/tex]
In this problem, the adjacent side is 4.3 and the hypotenuse is 6.7. Therefore, we have:
[tex]\[ \cos(x) = \frac{4.3}{6.7} \][/tex]
To find the measure of angle [tex]\(x\)[/tex]:
[tex]\[ x = \cos^{-1}\left(\frac{4.3}{6.7}\right) \][/tex]
Evaluating the expression:
[tex]\[ x \approx 0.8739648401891128 \][/tex]
Thus, [tex]\( x \)[/tex] is approximately [tex]\( 0.8739648401891128 \)[/tex] radians. This is the angle whose cosine is the ratio [tex]\(\frac{4.3}{6.7}\)[/tex].
To summarize, in the triangle, the angle [tex]\( x \)[/tex] is such that the cosine of [tex]\( x \)[/tex] equals the ratio of the length of the adjacent side (4.3) to the length of the hypotenuse (6.7). The precise measure of angle [tex]\( x \)[/tex] is approximately [tex]\( 0.8739648401891128 \)[/tex] radians or, in degrees, approximately \( 50.070561224 \( degrees.
