A central angle 𝜃 in a circle of radius 2 m is subtended by an arc of length 3 m. Find the measure of 𝜃 in degrees.

Question

A central angle 𝜃 in a circle of radius 2 m is subtended by an arc of length 3 m. Find the measure of 𝜃 in degrees. (Round your answer to one decimal place.)

𝜃 =   °

Find the measure of 𝜃 in radians. (Round your answer to two decimal places.)

𝜃 =   rad

Answer 1

Θ in radians:

As the relation of radius: r, arc: s and theta: Θ is;

=> s = rΘ

solving this equation for theta,

=> Θ = s / r

putting given values in this equation;

=> Θ = 3/2 = 1.5 rad ----> (1)

Θ in degree:

as we know the relation relation between degree and radian:

=> 2π rad = 360^o , rad = radian

=> 1 rad = 360/ 2* 3.14159 , π = 3.14159

=> 1 rad = 57.2958^o -----(2)

substituting the value of equation 2 in equation 1

=> Θ = 1.5 * 57.2958^o

=> Θ = 85.9437^o

Rounding to two decimal places.

=> Θ = 85.94^o