Question

I would appreciate some assistance on the equation it's honestly different then the others I've seen so far.

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for area of a sector

`Areaofsector=(\theta)/(360)*\pi r^2`

STEP 2: Write the given measures

`\begin{gathered} For\text{ Sector }COD \\ \theta=90\degree \\ radius(r)=? \\ Area\text{ }of\text{ }sector=50.24 \end{gathered}`

STEP 3: substitute the values in the formula in step 1

`50.24=(90)/(360)*3.14* r^2`

Solve for radius(r)

`\begin{gathered} 50.24=(90)/(360)*3.14r^(2) \\ 50.24=(282.6r^2)/(360) \\ \\ Cross\text{ Multiply} \\ 50.24*360=282.6r^2 \\ r^2=(18086.4)/(282.6) \\ r^2=64 \\ r=√(64)=8\text{ unit} \end{gathered}`

Therefore, the radius of the circle is 8 units

STEP 4: Calculate the measure of arc AB

`length\text{ }of\text{ }an\text{ }arc=(\theta)/(360)*2\pi r`

STEP 5: Write the known values

`\begin{gathered} \theta=30\degree \\ r=8 \\ \pi=3.14 \end{gathered}`

STEP 6: calculate the length of the arc

By substitution in to the formula in step 4, we have:

`\begin{gathered} (30)/(360)*2*3.14*8=(1507.2)/(360)=4.186666667 \\ length\approx4.2units \end{gathered}`

Hence, the measure of arc AB is approximately 4.2 units