Question

if the length of an arc is equal to half of the length of the radius of the circle,then the angle subtended by the arc at the centre in radians would be
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Answer 1

Answer:0.00873

Step-by-step explanation:

As

Theta equal to length of arc over radius

Where length l = 0.5

Radius r= 1

So

Angle = 0.5 °

In radians

Angle = 0.000873

Answer 2

Given:

Length of arc $=l$

Radius $=R$

Angle subtended by the arc = θ

To find:

The angle subtended by the arc when the length of the arc is half the radius.

Solution:

We know,

A complete circle subtends an angle of $360^{o}$ at the center and the length of the complete circle is nothing but its circumference.

Hence, we can say that an arc of length $2\pi R$ subtends a angle $360^{o}$.

Now,

If we consider a small part of the circle as sector of the circle, whose length is $l$ , and assume, that it subtends an angle θ at the center.

Now, we have,

$2\pi R$ subtends $360^{o}$

$l$ subtends θ

θ $=\frac{360^{o}*l }{2\pi R}$

θ $=\frac{l}{R}$

According to the question,

If the length of the arc is half of the length of the radius.

$l=\frac{R}{2}$

Substituting this value in the equation, we get

θ = $\frac{(\frac{R}{2}) }{R}$

θ $=0.5$°  $;$ $or$

θ $=0.00873$ $rad$

Final answer:

Hence, the angle subtended by the arc at the center will be 0.00873 radians.