Question

3. Find the measure of the angle subtended by an
arc of the length 38 mm at the centre of a circle
of radius 19 mm. answer me please... ​

Answer 1

Answer:

Angle Subtended by arc at the center is 115°.

Step-by-step explanation:

Given:

Length of the arc = 38 mm

Radius of the circle, r = 19 mm

To find: Measure of angle subtended by arc.

Formula for length of the arc = $\frac{\theta}{360^{\circ}}\times2\pi r$

So,

$length\:of\:arc=\frac{\theta}{360^{\circ}}\times2\pi r$

$38=\frac{\theta}{360}\times2\times3.14\times19$

$38=\frac{\theta}{360}\times119.32$

$\frac{38\times360}{119.32}=\theta$

$\theta=114.649681529$

$\theta=115$

Therefore, Angle Subtended by arc at the center is 115°.