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(a) What angle in radians is subtended by an arc that has a length of 1.75 m and is part of a circle with a radius of 1.10 m?

(b) Express the same angle in degrees.

(c) The angle between two radii of a circle is [tex]0.55 \text{ rad}[/tex]. What arc length is subtended if the radius is 2.40 m?

Answer :

The angle subtended by the arc is 1.59 rad and 91.146°. The arc length subtended by an angle of 0.55 rad with a radius of 2.4 m is 1.32 m.

(a) To find the angle in radians, we can use the formula:

angle = arc length / radius

Plugging in the values, we get:

angle = 1.75 m / 1.1 m = 1.59 rad

(b) To convert the angle from radians to degrees, we can use the formula:

angle in degrees = angle in radians * (180/pi)

Substituting the value, we get:

angle in degrees = 1.59 rad * (180/pi) = 91.146°

(c) To find the arc length, we can use the formula:

arc length = angle * radius

Plugging in the values, we get:

arc length = 0.55 rad * 2.4 m = 1.32 m

Learn more about the topic of Angles here:

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