Question

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 Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?

Answer 1

Answer:

the distance between Reshma and Mandip = 9.6 m

Step-by-step explanation:

Let call the point R , S & M where Reshma, Salma and Mandip are standing on Circle & call the center of Circle O

Then OR = OS = OM = 5 m  ( Radius of circle)

RS = 6 m

SM = 6 m

RM = ?

in ΔORS

RS² = OR² + OS² - 2*OR*OSCos∠ROS

=> 6² = 5² + 5² - 2*5*5*Cos∠ROS

=> 36 = 50 - 50Cos∠ROS

=> Cos∠ROS = 14/50

=>  Cos∠ROS = 0.28

=> Sin∠ROS = 0.96    (Sin²α = 1 - Cos²α)

Similarly Cos∠SOM  = 0.28

              Sin∠ROS = 0.96

∠MOR = 360° - ∠ROS - ∠SOM  or ∠ROS + ∠SOM

Taking Cos both Sides

=> Cos∠MOR = Cos(360° - ∠ROS - ∠SOM) or Cos(∠ROS + ∠SOM)

=> Cos∠MOR = Cos(∠ROS + ∠SOM)

=>  Cos∠MOR = Cos∠ROS .Cos∠SOM - Sin∠ROS . Sin∠SOM

=> Cos∠MOR =  0.28*0.28 - 0.96*.96

=> Cos∠MOR = - 0.8342

RM² = OM² + OR² - 2*OM*ORCos∠MOR

=> RM² = 50 - 50(- 0.8342)

=> RM² = 92.16

=> RM = 9.6

the distance between Reshma and Mandip = 9.6 m

Answer 2

Answer:

Here is the answer..........