SOLUTION: A ship leaves Sydney and travels due north for two hours at 24km/h, it then travels due east with the same speed. The ship passes buoy O first and then some time later passes buoy

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Question 1122441: A ship leaves Sydney and travels due north for two hours at 24km/h, it then travels due east with the same speed. The ship passes buoy O first and then some time later passes buoy P. The bearing of Sydney from buoy O is 240 degrees, and then from buoy P is 250 degrees. FInd the distance between the two buoys.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A ship leaves Sydney and travels due north for two hours at 24km/h, it then travels due east with the same speed.
The ship passes buoy O first and then some time later passes buoy P.
The bearing of Sydney from buoy O is 240 degrees, and then from buoy P is 250 degrees.
Find the distance between the two buoys.
:
Draw this out. You can see it forms two right triangles.
Northern distance: 2 * 24 = 48 km
the interior angle of the smaller triangle: 270 - 240 = 30 degrees
Use the tangent to find the eastern distance to point O, (a)
tan(30) = 48%2Fa
a = 83.14 km
then
the interior angle of the larger triangle: 270 - 250 = 20 degrees
Use the tangent to find the eastern distance to point P, (b)
tan(20) = 48%2Fb
a = 131.88 km
:
Distance from O to P: 131.88 - 83.14 = 48.74 km