A fish trawler travels 200km on a bearing of 077degree and then 150km on a bearing of 167 degree,find how far the trawler is from the starting point?
To find how far the trawler is from the starting point, we can use the law of cosines.
Let's call the starting point A, the first destination point B, and the second destination point C. We are trying to find the distance AC.
First, we need to find the internal angles of the triangle ABC. The angle at A is 180 - 90 = 90 degrees (since the vectors AB and AC are perpendicular to each other). Therefore, the angle at B is 167 - 90 = 77 degrees (using the information given in the problem), and the angle at C is 180 - 77 - 90 = 13 degrees (since the sum of angles in a triangle is 180 degrees).
Now, we can use the law of cosines to find the distance AC:
AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(C)
AC^2 = 200^2 + 150^2 - 2 * 200 * 150 * cos(13)
AC^2 = 40000 + 22500 - 60000 * cos(13)
AC^2 = 62500 - 60000 * cos(13)
AC^2 ≈ 62500 - 59539.4 (using a calculator to evaluate the cosine of 13 degrees)
AC^2 ≈ 960.6
AC ≈ sqrt(960.6)
AC ≈ 31 km
Therefore, the trawler is approximately 31 km away from the starting point.