Question

If the radius of a circle is 13 cm, what angle (in radians) is subtended by an arc of 10 cm?

a) 0.77 radians
b) 0.97 radians
c) 1.16 radians
d) 1.45 radians

Answer 1

The angle in radians subtended by a 10 cm arc in a circle with a radius of 13 cm is calculated using the formula θ = s / r, which gives approximately 0.77 radians.

Step-by-step explanation:

To determine the angle subtended by an arc of a circle in radians, the formula that relates the arc length (s), the radius (r), and the angle in radians (θ) is θ = s / r. For a circle with a radius of 13 cm and an arc length of 10 cm, the angle in radians can be calculated as follows: θ = 10 cm / 13 cm.

Performing the division yields θ = 0.769230769.... When rounded to two decimal places, this is approximately 0.77 radians, which is closest to option a).

So the angle in radians subtended by an arc of 10 cm in a circle with a radius of 13 cm is approximately 0.77 radians.