Question

Calculate the length of minor arc Ab with the angle 72 with a circumference of 90

Answer 1

18

Explanation:

here,

circumference of the circle = 90

`S = r\theta`

in above equation, S is the length of arch, r is the radius and theta is the angle formed by arc at the center,

As you can see, in a circle of given radius,

`S \propto \theta`

therefore,

`(S_1)/(S_2) = (\theta_1)/(\theta_2)`

we have the arc length for angle 360 (circumference of the circle).

let S1 be the length of minor arc, S2 be the arc formed by full circle (360 degree),

`(S_1)/(90) = (72)/(360)`

solving the above equation, we get

`S_1 = 18`