What is the measure in radians for the central angle of a circle whose radius is 6 cm and intercepted arc length is 5.4 cm? Enter your answer as a decimal in the box.

Question

asked Aug 26, 2020 193k views

2 Answers

Blamb · Answer 1 · 2020-08-30T10:52:21+0000

Answer:

0.9 RAD

Explanation:

Circumference of a circle is (2π * radius), in this case: 2*π*6 = 12π

In radians, a full circle of 360 degrees is 2π

We can easily say the arc of 5.4 cm has an equal proportion to the full circumference (12π) as the angle that generates it to the full circle (2π):

$(5.4)/(12\pi) = (x)/(2\pi)$

We multiply each side by 2π to simplify:

(5.4)/(6) = x

x = 5.4/6 or x = 0.9 rad