three girls Reshma Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park Reshma throws a ball to Salma Salma to Mandeep Mandeep to reshma if the distance of between Reshma and Salma and between Salma and Mandeep is 6m each what is the distance between reshma and Mandeep?
Answers
The distance between reshma and Mandeep = 9.6 m
Step-by-step explanation:
RAdius = 5 cm
Let call Reshma , Salam & Mandip standing point R , S & M respectively
and Center of Circle O
RS = 6 m
SM = 6 m
RM = ?
RO = SO = SM = 5 m ( radius of Circle)
in Δ RSO
=> RS² = RO² + SO² - 2*RO*OSCos∠ROS
=> 6² = 5² + 5² - 2 * 5 * 5 *Cos∠ROS
=> Cos∠ROS = 7/25
∠ROS = Cos⁻¹(7/25)
Similarly ∠SOM = Cos⁻¹(7/25)
Cos⁻¹(7/25) + Cos⁻¹(7/25) = 2 * Cos⁻¹(7/25)
in Δ RMO
RM² = RO² + OM² - 2 * RO * OM Cos(2 * Cos⁻¹(7/25))
=> RM² = 5² + 5² - 2 * 5 * 5 Cos(2 * Cos⁻¹(7/25))
Cos(2 * Cos⁻¹(7/25))
let say Cos⁻¹(7/25) = x
=> Cos x = 7/25
Cos2x = 2Cos²x - 1
=> Cos2x = 2(7/25)² - 1
=> Cos2x = (98 - 625)/625
=> Cos2x = -527 /625
=> Cos(2 * Cos⁻¹(7/25)) = -527 /625
RM² = 50 - 2 * 5 * 5 ( -527 /625)
=> RM² = 50 + 1054/25
=> RM² = 2304/25
=> RM = 48/5
=> RM = 9.6
the distance between reshma and Mandeep = 9.6 m
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