To answer this question we will use the following formula for the arc length of a central angle θ degrees:
[tex]\begin{gathered} \frac{\theta}{180}\cdot\pi r, \\ \text{where r is the circumference's radius.} \end{gathered}[/tex]
Assuming that Y is the circumference's center we get:
[tex]m\hat{AM}+m\hat{MH}=180^{\circ}.[/tex]
Substituting mMH=88degrees we get:
[tex]m\hat{AM}+88^{\circ}=180^{\circ}\text{.}[/tex]
Therefore:
[tex]\text{m}\hat{\text{AM}}=92^{\circ}\text{.}[/tex]
Then the arc length of MA is:
[tex]\frac{92}{180}\cdot\pi\cdot16m\approx8.18\pi m\approx25.69m\text{.}[/tex]
Answer: First option.
