Question

Identify the arc length of MA in terms of pi and rounded to the nearest hundredth.

Answer 1

To answer this question we will use the following formula for the arc length of a central angle θ degrees:

`\begin{gathered} (\theta)/(180)\cdot\pi r, \\ \text{where r is the circumference's radius.} \end{gathered}`

Assuming that Y is the circumference's center we get:

`m\hat{AM}+m\hat{MH}=180^(\circ).`

Substituting mMH=88degrees we get:

`m\hat{AM}+88^(\circ)=180^(\circ)\text{.}`

Therefore:

`\text{m}\hat{\text{AM}}=92^(\circ)\text{.}`

Then the arc length of MA is:

`(92)/(180)\cdot\pi\cdot16m\approx8.18\pi m\approx25.69m\text{.}`

Answer: First option.