Question

An arc of length 2.2 cm subtends an angle θ at the centre of the circle with radius 2.8 cm. The value of θ is ______.

Options

• 50°

• 60°

• 45°

• 30°

Answer 1

An arc of length 2.2 cm subtends an angle θ at the centre of the circle with radius 2.8 cm. The value of θ is 45°.

Explanation:

Given: Arc length `l` = 2.2 cm 

Radius r = 2.8 cm

Using `π = 22/7`:

Length of arc (`l`) is given by:

`l = θ/360^circ xx 2πr`

`2.2 = θ/360^circ xx 2 xx 22/7 xx 2.8`

`2.2 = θ/360^circ xx 44 xx 0.4`

`2.2 = θ/360^circ xx 17.6`

`θ = (2.2 xx 360^circ)/17.6`

`θ = 360^circ/8`

θ = 45°