Respuesta :
a. Angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of radius 2.50 m is equals to 34.4°.
b. Radius of the circle with an arc 14.0 cm long on the circumference of a circle subtends an angle of 128° is equals to 6.27cm.
What is length of an arc?
" Length of an arc is defined as the part of the circumference between the two radii of the circle with subtended angle."
Formula used
Length of an arc 'l' = rθ
r = radius of the circle
θ = Subtended angle between two radii.
According to the question,
a. Given ,
Length of an arc 'l' = 1.50m
Radius of the circle 'r' = 2.50m
Substitute the value in the formula to get subtended angle,
[tex]1.50 = (2.50) \theta[/tex]
⇒ [tex]\theta = \frac{1.50}{2.50}[/tex]
⇒[tex]\theta = 0.6[/tex] radians
⇒[tex]\theta= (0.6)\frac{180}{\pi }[/tex]
⇒[tex]\theta = 34.4[/tex] degrees
b. Given ,
Length of an arc 'l' = 14cm
Subtended angle = 128°.
Substitute the value in the formula to get radius of the circle 'r' ,
14 = r × 128°
⇒[tex]r = \frac{14}{128}[/tex]
⇒[tex]r= \frac{14}{\frac{\pi }{180} (128)}[/tex]
⇒[tex]r= \frac{(14) (180)}{128\pi }[/tex]
⇒[tex]r= 6.27[/tex]cm
c. incomplete information
Therefore,
a. Angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of radius 2.50 m is equals to 34.4°.
b. Radius of the circle with an arc 14.0 cm long on the circumference of a circle subtends an angle of 128° is equals to 6.27cm.
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