Answer: In degrees , The measure of [tex]\theta=65.5^{\circ}[/tex]
In radians , the measure of [tex]\theta =\dfrac{8}{7}\text{ radians}[/tex].
Step-by-step explanation:
We know that the formula for length of arc is given by :-
[tex]l=\theta r[/tex]
, where [tex]\theta[/tex] = Central angle subtended by arc.
r= radius of the circle.
As per given , we have
Radius of circle : r=7 m
Length of arc : l= 8 m
Substitute these values in the above formula , we get
[tex]8=\theta (7)\\\\\Rightarrow\ \theta =\dfrac{8}{7}\text{ radians}[/tex]
Hence, the measure of [tex]\theta =\dfrac{8}{7}\text{ radians}[/tex].
To convert it into degrees we multiply it with [tex]\dfrac{180^{\circ}}{\pi}[/tex]
The measure of [tex]\theta =\dfrac{8}{7}\times\dfrac{180^{\circ}}{\pi}[/tex]
[tex]=(\dfrac{8\times180}{7\times3.14})^{\circ}=65.5141037307^{\circ}[/tex]
[tex]\approx65.5^{\circ}[/tex]
Hence, the measure of [tex]\theta=65.5^{\circ}[/tex]
The measure of central angle theta in a circle of radius 7 m and subtended by an arc of length 8 m is 65. 4°(degrees) or 1.141445 radians
The central angle is unknown and its is subtended by an arc of length 8m .
Therefore,
Using length of arc formula,
length of arc = ∅ /360 × 2πr
where
∅ = angle
r = radius = 7m
length of arc = 8m
8 = ∅ /360 × 2 × 7 × π
8 = ∅ /360 × 14π
14π∅ = 2880
∅ = 2880 / 14π
∅ = 65.3912348499
∅ ≈ 65. 4°(degrees)
∅ = 1.141445 radians
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