A circular ring of diameter 10 cm is suspended by means of 6 equal threads attached at equal intervals on its circumference. The point of suspension is 12 cm above the centre. Find the cosine of the angle between two successive threads.
Answers
Given : A circular ring of diameter 10 cm is suspended by means of 6 equal threads attached at equal intervals on its circumference. The point of suspension is 12 cm above the centre
To find : the cosine of the angle between two successive threads.
Solution:
A circular ring of diameter 10 cm
=> Radius = 5 cm
point of suspension is 12 cm above center
Hence thread length = √5² + 12² = 13 cm
6 equal threads attached at equal intervals
=> Angle at center from attached point of consecutive threads = 360/6 = 60°
Hence base point of consecutive threads and center from an equilateral triangle
=> distance between base of two consecutive threads = radius = 5 cm
While thread length = 13 cm
applying cosine Formula
c² = a² + b² - 2abCosC
=> 5² = 13² + 13² - 2(13)(13)CosC
=>25 = 2 * 169 ( 1 - CosC)
=> 25/338 = 1 - CosC
=> CosC = 1 - 25/338
=> CosC = 313/338
the cosine of the angle between two successive threads. = 313/338
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