To solve the equation \(\frac{\pi}{6} = 15\), we need to determine if there is a value that satisfies this equation. Let's break down the steps required.
1. Understanding the Equation:
[tex]\[\frac{\pi}{6} = 15.\][/tex]
2. Isolating \(\pi\):
Multiply both sides of the equation by 6 to clear the fraction:
[tex]\[ \pi = 15 \times 6.\][/tex]
3. Performing the Multiplication:
Calculate the right side:
[tex]\[15 \times 6 = 90.\][/tex]
This yields:
[tex]\[\pi = 90.\][/tex]
4. Verifying the Solution:
We understand \(\pi\) is approximately 3.14159. Thus:
[tex]\[\pi \approx 3.14159.\][/tex]
The value \(90\) is quite different from \(3.14159\).
5. Conclusion:
There is no value of \(\pi\) that can satisfy \(\pi = 90\). Therefore, there is no solution to the equation \(\frac{\pi}{6} = 15\).
The equation \(\frac{\pi}{6} = 15\) results in a contradiction since \(\pi\) is a fixed irrational number approximately equal to 3.14159 and cannot possibly be 90. Hence, the solution set is:
[tex]\[ \text{EmptySet.} \][/tex]
Therefore, none of the given values [tex]\(x = 20\)[/tex], [tex]\(x = 3\)[/tex], or [tex]\(x = 75\)[/tex] is a solution to the equation [tex]\(\frac{\pi}{6} = 15\)[/tex].
