Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
I need your help in another trigonometric problem?
From a lighthouse a boat was sighted at sea with a bearing of N12°W (North 12 degrees West). The boat was traveling due east at 12 knots per hour. Fifteen minutes later it had bearing at N72°E (North 72 degrees East). How far was the boat from the lighthouse when last sighted?
1 Answer
- Adrian SLv 710 years agoFavorite Answer
OK. Draw a picture with lighthouse as the vertex at the bottom of the triangle. Then put a dot at a point 12 degrees west of north and connect that line to lighthouse. Now true North is vertical from lighthouse so there is a right triangle formed between the lighthouse, the point 12 degrees west of north and true north east of the original boat location. Now, you can get the angle formed by the vertex of the boat, lighthouse and due east as 90-12 = 78 degrees.
In 15 minutes the boat has traveled 12/4 = 3 nautical miles. but the angle from due north is now 72 degrees. Complete the triangle using the boat's old position, new position and lighthouse.
You know the lighthouse vertex angle is 72+12 = 84 degrees and you know the vertex angle between the boat's old position, lighthouse and due east is 78 degrees.
Now use Law of Sines to get the leg of the completed triangle that gives the distance from boat at new position from lighthouse. 3/sin84 = x/sin78 and your answer should be 2.95 nautical miles.
Source(s): Math tutor for several years.
