Question

The ratio of two angles subtended by two arcs of unequal lengths at the centre is 5:2 and
if the sexagesimal value of the second angle is 30°, then let us determine the sexagesimal
value and the circular value of the first angle.​

Answer 1

Answer:

θ = 75°

Step-by-step explanation:

let the length of arcs be 5x and 2x

Let r be the radius of the circle

⇒ 30* π/180*r = 2x …[1]

Let θ be the angle subtended by the arc of length 5x.

⇒ θ*r = 5x …[2]

By dividing eq. [1] and eq. [2]

π/6 = 2 θ/5

⇒ θ = 5π/12

⇒ θ = 5π/12 * 180/π

⇒ θ = 75°

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