To find the Length of MKL, we need to find the length of JM and JL using the length of an arc formula
[tex]\begin{gathered} \text{Length of arc =}\frac{\theta}{360}\times2\pi r \\ \text{where r=MK/2 =5m} \end{gathered}[/tex]
STEP 1
Find the angle subtended at N and find the arc JM
N +52= 180 -------sum of angles on a straight line.
N= 180-52
N=128
[tex]\begin{gathered} JM=\frac{128}{360}\times2\times3.14\times5 \\ JM=11.164 \end{gathered}[/tex]
STEP 2
Find the length of JL
The angle subtended at Therefore,
[tex]\begin{gathered} JL=\frac{90}{360}\times2\times3.14\times5 \\ JL=7.85 \end{gathered}[/tex]
STEP 3
Find the lenght of MKL. MKL is the sum of JM and JL
[tex]\begin{gathered} \text{MKL}=11.164+7.85 \\ =19.01 \end{gathered}[/tex]
The answer is 19.01m
