Two ships leave a Port O. One ship travels on a bearing of 3400 to a point P which is 50 km from O. The other ship travels on a bearing of 0600 to a point Q, 85 km from O. (a) Draw a diagram to represent the position of the port and the two ships. On your diagram, carefully label North, the given angles and the distances travelled. (b) Calculate the distance PQ in km (c) Determine the bearing of P from Q.
Two ships leave a Port O. One ship travels on a bearing of 3400 to a point P which is 50 km from O. The other ship travels on a bearing of 0600 to a point Q, 85 km from O. (a) Draw a diagram to represent the position of the port and the two ships. On your diagram, carefully label North, the given angles and the distances travelled. (b) Calculate the distance PQ in km (c) Determine the bearing of P from Q.
I'm assuming that 3400 = 340.0 and that 0600 = 60.0
Then the angle between them is just 80°
We can use the Law of Cosines to find PQ =
PQ^2 = 85^2 + 50^2 - 2(85)(50)cos(80)
PQ^2 = 8248.9904898305
PQ = about 90.824 km
And the bearing from P to Q is given by [90 + sin-1(4.485/90.824)]° = [90 + 2.83]° = 92.83°
Here's a diagram.....("North" is at the "top' )
Two ships leave a Port O. One ship travels on a bearing of 3400 to a point P which is 50 km from O. The other ship travels on a bearing of 0600 to a point Q, 85 km from O. (a) Draw a diagram to represent the position of the port and the two ships. On your diagram, carefully label North, the given angles and the distances travelled. (b) Calculate the distance PQ in km (c) Determine the bearing of P from Q.
I'm assuming that 3400 = 340.0 and that 0600 = 60.0
Then the angle between them is just 80°
We can use the Law of Cosines to find PQ =
PQ^2 = 85^2 + 50^2 - 2(85)(50)cos(80)
PQ^2 = 8248.9904898305
PQ = about 90.824 km
And the bearing from P to Q is given by [90 + sin-1(4.485/90.824)]° = [90 + 2.83]° = 92.83°
Here's a diagram.....("North" is at the "top' )