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Answer :
To find the angle subtended by an arc in radians, we can use the formula θ = s/r, where θ is the angle in radians, s is the length of the arc, and r is the radius of the circle. To convert the angle to degrees, we can use the formula θ(degree) = θ(rad) * 180/π. To find the radius of a circle with an arc length and angle given, we can rearrange the formula θ = s/r to solve for r. To find the length of the intercepted arc on the circumference of a circle, we can use the formula s = r * θ.
To find the angle subtended by an arc in radians, we can use the formula θ = s/r, where θ is the angle in radians, s is the length of the arc, and r is the radius of the circle.
a) To find the angle in radians of an arc of 1.57m on a circle with radius 2.45m, we have θ = 1.57/2.45 ≈ 0.642 rad.
b) To convert the angle to degrees, we can use the formula θ(degree) = θ(rad) * 180/π. So the angle in degrees is 0.642 * 180/π ≈ 36.82°.
c) To find the radius of a circle with an arc length of 13.3cm and an angle of 125°, we can rearrange the formula θ = s/r to solve for r. So, r = s/θ = 13.3/125 ≈ 0.1064m.
d) To find the length of the intercepted arc on the circumference of a circle with an angle of 0.800 rad and radius of 1.60m, we can use the formula s = r * θ. So, the length of the arc is 1.60 * 0.800 ≈ 1.28m.
Complete question :-
a)What angle in radians is subtended by an arc of 1.57m in length on the circumference of a circle of radius 2.45m ?
b)What is this angle in degrees?
c)An arc of length 13.3cm on the circumference of a circle subtends an angle of 125°? What is the radius of the circle?
d)The angle between two radii of a circle with radius 1.60m is 0.800rad. What length of arc is intercepted on the circumference of the circle by the two radii?
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Rewritten by : Jeany
Final answer:
To find the angle in radians, use the formula angle = arc length / radius. To convert radians to degrees, multiply by 180/pi. To find the radius, use the formula radius = arc length / (angle in degrees × (π / 180)). To find the arc length, use the formula arc length = angle × radius.
Explanation:
To find the angle in radians, we need to use the formula: angle = arc length / radius. In the first part of the question, the arc length is given as 1.57 m and the radius is 2.45 m. So, the angle in radians would be 1.57 / 2.45 = 0.641 rad. To convert this angle to degrees, we use the conversion factor 1 radian = 180 degrees. So, the angle in degrees would be 0.641 × 180 = 115.78 degrees.
In the second part of the question, the arc length is given as 13.3 cm and the angle in degrees is 125 degrees. We can find the radius using the formula: radius = arc length / (angle in degrees × (π / 180)). Plugging in the values, we get radius = 13.3 / (125 × (π / 180)) = 1.023 cm.
In the third part of the question, the angle in radians is given as 0.800 rad and the radius is 1.60 m. We can find the length of the arc using the formula: arc length = angle × radius. Plugging in the values, we get arc length = 0.800 × 1.60 = 1.28 m.
