To determine in which triangle the value of \(x\) is equal to \(\cos^{-1}\left(\frac{4.3}{6.7}\right)\), follow these steps.
### Step-by-Step Solution:
1. Identify the Given Values:
- We have a triangle where the side opposite the angle \(x\) is 4.3 units.
- The hypotenuse of the triangle is 6.7 units.
2. Use the Inverse Cosine Function:
- We need to calculate the angle \(x\) using the inverse cosine (arccos) function.
- The ratio of the side opposite \(x\) to the hypotenuse is \(\frac{4.3}{6.7}\).
3. Calculate the Angle \(x\):
- \(x = \cos^{-1}\left(\frac{4.3}{6.7}\right)\).
4. Numerical Calculation:
- Using the inverse cosine function, we find
[tex]\[
x \approx 0.8739648401891128 \text{ radians}.
\][/tex]
5. Convert the Angle to Degrees:
- To convert radians to degrees, multiply by \(\frac{180}{\pi}\):
[tex]\[
x \approx 0.8739648401891128 \times \frac{180}{\pi} \approx 50.07449678566164 \text{ degrees}.
\][/tex]
### Interpretation of Results:
- The angle \(x\) in the triangle is approximately \(0.874\) radians or \(50.074\) degrees.
- This value of \(x\) corresponds to a triangle where the side opposite the angle \(x\) (opposite side) is 4.3 units and the hypotenuse is 6.7 units.
### Conclusion:
The triangle in question is the one where the value of [tex]\(x\)[/tex] is calculated based on [tex]\(\cos^{-1}\left(\frac{4.3}{6.7}\right)\)[/tex], resulting in an angle of approximately [tex]\(50.074\)[/tex] degrees. Therefore, in a triangle with a hypotenuse of 6.7 units and an opposite side of 4.3 units, the angle [tex]\(x\)[/tex] will be approximately [tex]\(50.074\)[/tex] degrees.
