A ship travels 62 km on a bearing of 12 degrees, and then travels on a bearing of 102 degrees for 111 km. Find the distance from
the starting point to the end of the trip, to the nearest kilometer. Show your work.
1 answer:
A bearing is an angle measured from the North.
The diagram should be something like that given above. (Note that the angles may not be measured accurately).
The diagram is drawn as follows:
1. The ship travels on a bearing of 12 degrees from the North line first so measure 12 degrees from the North line.
2. Then from that point, after it travels 62 km, the ship goes on a bearing of 102 degrees so draw another imaginary north line, and measure 102 degrees from it.
The diagram now takes shape of a triangle. Use the cosine rule to find the missing side (marked x km). Here is how I do the cosine rule:
First find the missing angle at the top of the triangle: 180 - 102 = 78 degrees. (Angles on a straight line add up to 180 degrees)
So, remember this formula:
Suppose the missing side is: c^2.
c^2 = a^2 + b^2 - (2ab cosC)
If you look at the diagram above, the angle C and the sides a, b, and c have been marked.
Use the formula given above and find the side c (that's the question you have been asked).
c^2 = 62^2 + 111^2 - (2(62)(111) cos 78)
c^2 = ANS (a very long number - better if you don't round off a number in the middle of an equation)
c = square root of ANS (following the rules of Algebra)
c = 115.34 km or simply 115 km
So the distance between the starting point to the end of the trip is 115 km.
The diagram should be something like that given above. (Note that the angles may not be measured accurately).
The diagram is drawn as follows:
1. The ship travels on a bearing of 12 degrees from the North line first so measure 12 degrees from the North line.
2. Then from that point, after it travels 62 km, the ship goes on a bearing of 102 degrees so draw another imaginary north line, and measure 102 degrees from it.
The diagram now takes shape of a triangle. Use the cosine rule to find the missing side (marked x km). Here is how I do the cosine rule:
First find the missing angle at the top of the triangle: 180 - 102 = 78 degrees. (Angles on a straight line add up to 180 degrees)
So, remember this formula:
Suppose the missing side is: c^2.
c^2 = a^2 + b^2 - (2ab cosC)
If you look at the diagram above, the angle C and the sides a, b, and c have been marked.
Use the formula given above and find the side c (that's the question you have been asked).
c^2 = 62^2 + 111^2 - (2(62)(111) cos 78)
c^2 = ANS (a very long number - better if you don't round off a number in the middle of an equation)
c = square root of ANS (following the rules of Algebra)
c = 115.34 km or simply 115 km
So the distance between the starting point to the end of the trip is 115 km.
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