Ship A is 72 miles from a light house on a shore. Its bearing from the lighthouse is N 15 degrees E. Ship B is 81 miles from the same lighthouse. Its bearing is N 52 degrees E. Find the number of miles between the two ships.
2007-03-18 06:09:30 · 7 answers · asked by stacie c 3 in Science & Mathematics ➔ Mathematics
Hi,
The difference between the 2 angles 52 - 15 or 37 degrees is the angle between the 2 measured distances. That gives you a triangle with 2 sides with lengths of 72 and 81 and the included angle of the triangle is 37 degrees. You can now use the Law of Cosines to find the distance between the 2 ships. That law is:
c^2 = a^2 + b^2 -2ab cos C
c^2 = 72^2 + 81^2 -2(72)(81)cos 37degrees
c = 49.29 miles This is the distance between the 2 ships!
I hope that helps.
2007-03-18 06:19:20 · answer #1 · answered by Pi R Squared 7 · 0⤊ 0⤋
take the lighthouse as a start point. draw a line to ship A, and call it point A. Then from ship A draw a line straight to the absolute north, and another line straight to the east. You get a ninety degree angle, with the line to the light house across it.
Moving over to the west, draw a line from the light house to Ship B. Then from ship B draw a line straight to the absolute north and another line straight to the east. You get another right angle 90 degrees with the line from the light house to ship B in the middle.
If you look at it a different way, you have one right angle triangle between each ship and the light house, with the bearing as the top angle .
You have a right angle triangle from the light house to Ship A, with the length of the side as 72, and the angle as 15. You have a right angle triangle to Ship B with the length of the side as 81, and the top angle as 52.
the triangles are parallel, and using these two triangles you need to calculate the length between Ship A and Ship B.
2007-03-18 06:41:19 · answer #2 · answered by sam_alot 2 · 0⤊ 0⤋
We normally draw this sort of situation with North up the page. Everything is East and North of the lighthouse so represent it by a dot low down on the left of the page. (An L next to it might help.) Now draw a straight line from it upwards and label it N. (It doesn't matter if it is not perfectly up the page.) Using a protractor measure 15 degrees from this line clockwise and draw in a line from the lighthouse in this direction. Measure along it 72 units (mm might be best) and mark a dot here with A beside it. Now measure 52 degrees clockwise from the line up the page and draw another line from the lighthouse. Measure 81mm along it and mark a dot with B beside it. You could find the distance between the ships approximately by measuring between them and using your scale. However, if you are learning trigonometry you may be expected to calculate the answer using the cosine rule for triangles.
Diagram in the first answer is nothing like correct. Also diagram given in the previous link is not correct because he shows angles measured anticlockwise from East. They should be measured clockwise from North. You may like to know that the military way of giving bearings ALWAYS does this so they never bother to give N and E etc, they would just say that the bearings are 015 and 052. Bearings past south would be over 180. One degree left of north would be 359.
2007-03-18 06:24:40 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Lighthouse --------- 81 miles-------- Ship B
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72miles
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Ship A
Just adjust the angles making 90 degrees = North, 0 degrees (on the right) is east and so on. Then use Law of cosines to find the number of miles.
2007-03-18 06:17:06 · answer #4 · answered by flit 4 · 0⤊ 0⤋
In triangle ABL
>ALB =37 degrees. (52-15)
AL = 72 miles
BL = 81 miles
Solve for AB using Law of Cosines for SAS
AB = 53.077401 miles
2007-03-18 07:16:44 · answer #5 · answered by ? 5 · 0⤊ 0⤋
enable us to call the finest of the mound M and the element right away below M and on the similar aspect (undeniable) as C and D should be G. Draw your self a photo to help understand. M is right away above G and G C D is a in the present day line with the criteria in that order. D has a smaller perspective of melancholy so should be more advantageous away than C in the right perspective triangle MGC the perspective GMC is 40 9°40 2'. in the right perspective triangle MGD the perspective GMD is 26°27'. utilizing the basic trigonometric applications you are able to calculate the length of the strains GC and GD. The length of CD is GD - GC. favor this facilitates get you on the right music.
2016-11-26 20:36:46 · answer #6 · answered by ? 4 · 0⤊ 0⤋
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2007-03-18 06:22:48 · answer #7 · answered by Second Newton... 2 · 0⤊ 0⤋