SOLUTION: The posts of a hockey goal are 2.0 m apart. A player attempts to score by shooting the puck along the ice from a point 12.0 m from one post and 10.1 m from the other. Within what
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Question 1159349: The posts of a hockey goal are 2.0 m apart. A player attempts to score by shooting the puck along the ice from a point 12.0 m from one post and 10.1 m from the other. Within what angle theta must the shot be made? Round your answer to the nearest degree Answer by jim_thompson5910(35256) (Show Source):
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Diagram
Points A and B are the goal posts
Point C is the player's position
Angle C = theta is the angle in which sweeps out the possible places to shoot the puck in between the goal posts
Use the law of cosines to find angle C
c^2 = a^2 + b^2 - 2*a*b*cos(C)
(2)^2 = (10.1)^2 + (12)^2 - 2*(10.1)*(12)*cos(C)
4 = 102.01 + 144 - 242.4*cos(C)
4 = 246.01 - 242.4*cos(C)
246.01 - 242.4*cos(C) = 4
-242.4*cos(C) = 4-246.01
-242.4*cos(C) = -242.01
cos(C) = -242.01/(-242.4)
cos(C) = 0.99839108910891 approximately
C = arccos(0.99839108910891)
C = 3.25058757974158 also approximate; make sure your calculator is in degree mode
When rounding to the nearest whole number, we then get C = 3 degrees
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