Question

An arc of length 28cm subtends an angle of 24 degree at the centre of a circle. in the same circle, what angle does an arc of length 35cm subtend

Answer 1

Answer:

30 degree

Step-by-step explanation:

24 degree = 28cm

x degree = 35cm

x= (35*24)/28= 30degrees

Answer 2

Answer:

Angle subtended by an arc of length 35cm is 30°.

Step-by-step explanation:

Given : Arc length = 28cm, θ = 24° and  arc length = 35cm.

To find :  The angle subtended by an arc of length 35cm.

Solution :

Arc length is the distance between two points along a section of a curve. Arc length is the distance around an arc.

• An  arc of a circle is a section of the circumference of the circle between two radii.

• The angle  subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc.

• Arc length, s, of a circle of radius, r, with central angle, θ, is given by

s = θ×r, where s is arc length, θ-central angle in radian ,r-radius .

• The arc length of a circle can be calculated with the radius and central angle using the arc length formula,

Length of an arc = θ×r, where θ is in radian.

                     and =  θ ×2πr,  or θ  ×πd , where θ is in degree.

                                360°            360°

Here, arc length  of a circle = 28cm

length of an arc = θ   × 2πr

                             360°  

24° × 2×π×r = 28

 360°

( 4 /60)×2×π×r = 28

(4/30) ×π×r = 28

 r = 28 ×(30/4) ×1/π = 7×30 ×1/π = 210/π cm.

Now in the same circle,  the length of an arc = 35cm.

                                              θ ×2πr = 35

                                             360°

       ⇒         θ = 35×360      = 35×180π = 5×180/30

                          2π×210/π       π×210

                  θ =  5×6 = 30° .

Thus the angle subtended by an arc of length 35cm is 30°.

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