Question

Ex 5.5

6. find the length of the chord cut off by an angle of π/6 subtended at the centre of a circle with radius 5cm

Answer 1

;
2 × 5 × sin( π / 12 ) = 10 × sin ( π / 12 ) ;

π/12 = ( 180° ) / 12 = 15°.

But, sin ( π/12 )

= sin 15°

= sin ( 45° - 30°)

= sin 45°· cos 30° - cos 45°· sin 30°

= (1/√2)·(√3 /2 ) - (1/√2)·(1/2)

= ( √3 - 1 ) / (2√2) =
`(( √(6)- √(2) ))/(4)` ;

Finally, ( 2.5 ) × ( 2.4 - 1.4 ) = 2.5 cm ;