Answer:
Arc length MK = 15.45 units (nearest hundredth)
Arc measure = 58.24°
Step-by-step explanation:
Calculate the measure of the angle KLN (as this equals m∠KLM which is the measure of arc MK)
ΔKNL is a right triangle, so we can use the cos trig ratio to find ∠KLM:
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
- [tex]\theta[/tex] is the angle
- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
Given:
- [tex]\theta[/tex] = ∠KLM
- A = LN = 8
- H = KL = 15.2
[tex]\implies \sf \cos(KLM)=\dfrac{8}{15.2}[/tex]
[tex]\implies \sf \angle KLM=\cos^{-1}\left(\dfrac{8}{15.2}\right)[/tex]
[tex]\implies \sf \angle KLM=58.24313614^{\circ}[/tex]
Therefore, the measure of arc MK = 58.24° (nearest hundredth)
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle)}[/tex]
Given:
- r = 15.2
- ∠KLM = 58.24313614°
[tex]\implies \textsf{Arc length MK}=2 \pi (15.2)\left(\dfrac{\sf \angle KLM}{360^{\circ}}\right)[/tex]
[tex]\implies \textsf{Arc length MK}=\sf 15.45132428\:units[/tex]
