Answer:
Therefore,
[tex]m\angle KLM\approx53\°[/tex]
Step-by-step explanation:
Given:
KM = 8
r = 5
To Find:
m∠KLM = ?
Solution:
Chord length formula is given by
[tex]\textrm{Chord length}=2r\sin (\dfrac{\theta}{2})[/tex]
where r is the radius of the circle and
'θ' is the angle from the center of the circle to the two points of the chord.
Let m∠KOM = θ be the center angle , Chord length = KM =8
So on Substituting the values we get
[tex]8=2\times 5\sin (\dfrac{\theta}{2})\\\\\dfrac{\theta}{2}=\sin^{-1}(0.8)=53.13\\\\\therefore \theta=106.26[/tex]
m∠KOM = θ = 106.3
Now by Inscribed angle theorem we have
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.
Therefore
[tex]m\angle KLM=\dfrac{1}{2}(m\angle KOM)[/tex]
Substituting the values we get
[tex]m\angle KLM=\dfrac{1}{2}(106.3)[/tex]
Therefore,
[tex]m\angle KLM\approx53\°[/tex]
