SOLUTION: A certain bridge 11 km long connects city A in the south and city B in the north. The true bearing of a small boat is 120 degrees from A. The distance between the boat and A is 15
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Question 772668: A certain bridge 11 km long connects city A in the south and city B in the north. The true bearing of a small boat is 120 degrees from A. The distance between the boat and A is 15 KM. Find the distance between the boat and B?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A certain bridge 11 km long connects city A in the south and city B in the north.
The true bearing of a small boat is 120 degrees from A.
The distance between the boat and A is 15 KM. Find the distance between the boat and B?
;
A triangle is formed by:
line AB, call it c (11 km)
line from boat to A, call it b (15 km)
line from boat to B, call it a, the distance from the boat to B
:
The north reference line is parallel to the line between A and B, from this we
can determine the interior angle at A; 180 - 120 = 60 degrees
:
Use the law of cosines, a^2 = b^2 + c^2 - 2(bc) cos(A)
a^2 = 15^2 + 11^2 - 2(15*11)cos(60)
a^2 = 225 + 121 - 2(165)*.5
a^2 = 346 - 165
a =
a = 13.453 km between the boat and B
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