Question

Raju and Babu are standing at the starting point A of a circular track of radius 20 metres.Raju walks through the arc AB and Babu walks through the chord AB,and reach B, If the central angle is 160 degree,how much distance did Raju walks more than Babu?​

Answer 1

Given : Raju and Babu are standing at the starting point A of a circular track of radius 20 metres.Raju walks through the arc AB and Babu walks through the chord AB,and reach B

central angle is 160 degree

To Find : how much distance did Raju walks more than Babu

Solution:

Radius = 20 m

central angle is 160°

Arc AB =  ( 160° / 360°) 2π Radius

= (4/9) 2 * 3.14 * 20

= 55.8  m

Raju walks = 55.8  m

Using Cosine rule

AB²  = OA² + OB² - 2.OA.OB Cos160°

OA = OB = Radius = 20

=> AB² = 20² + 20²  - 2*20² Cos160

=> AB² = 20² ( 2 - 2Cos160)

=> AB² = 20² ( 3.88)

=> AB = 20* 1.97

=> AB = 39.4

Babu Walks =  39.4 m

Raju walks more than Babu = 55.8 - 39.4

= 16.4 m

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