A hockey player takes aim at the goalie net, whose posts are 2.0 m apart. The player is 7.0 m from one post and 8.2 m from the other post. Within what angle does the player have to shoot the puck in order to get it in the net?
To find the angle within which the player needs to shoot the puck, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite side c, the following equation holds true:
c² = a² + b² - 2abcos(C)
In this case, the sides of the triangle are 7.0 m, 8.2 m, and 2.0 m, and we want to find the angle C (which is the angle within which the player needs to shoot the puck):
2.0² = 7.0² + 8.2² - 2(7.0)(8.2)cos(C)
4 = 49 + 67.24 - 114.8cos(C)
4 = 116.24 - 114.8cos(C)
114.8cos(C) = 112.24
cos(C) = 112.24 / 114.8
cos(C) ≈ 0.9767
C ≈ cos^(-1)(0.9767)
C ≈ 11.01 degrees
So, the player has to shoot the puck within an angle of approximately 11.01 degrees to get it in the net.
hey bot
how did you get 112.24 / 114.8 = 0.9767 ??
Apologies for the mistake. Let's recalculate it correctly:
4 = 116.24 - 114.8cos(C)
114.8cos(C) = 112.24
cos(C) = 112.24 / 114.8
cos(C) ≈ 0.9764
Now, finding the inverse cosine of 0.9764:
C ≈ cos^(-1)(0.9764)
C ≈ 12.99 degrees
Therefore, the correct answer is approximately 12.99 degrees.
You made the same mistake
better have your division algorithm checked out
Apologies for the repeated mistake.
Let's recalculate it correctly:
4 = 116.24 - 114.8cos(C)
114.8cos(C) = 116.24 - 4
114.8cos(C) = 112.24
cos(C) = 112.24 / 114.8
cos(C) ≈ 0.9769
Now, finding the inverse cosine of 0.9769:
C ≈ cos^(-1)(0.9769)
C ≈ 11.21 degrees
Therefore, the correct answer is approximately 11.21 degrees.
well, 3 tries at 112.24/114.8 and wrong each time
I get .9777003...
and my angle is 12.12 , not 12.21
you are really off your game today!!!
Apologies for the repeated errors. Let's recalculate it correctly:
4 = 116.24 - 114.8cos(C)
114.8cos(C) = 116.24 - 4
114.8cos(C) = 112.24
cos(C) = 112.24 / 114.8
cos(C) ≈ 0.9777
Now, finding the inverse cosine of 0.9777:
C ≈ cos^(-1)(0.9777)
C ≈ 12.12 degrees
Therefore, the correct answer is approximately 12.12 degrees.