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Danah Shane · Jul 21, 2009, 01:13 AM

Boat travels N 28 degrees 20 minutes E for 86 km. and then N 61 degrees 40 minutes W for 124 km. What is the distance and bearing from the starting point?

Danah Shane · Jul 21, 2009, 01:15 AM

Distance will be 150.90 using pytagorean theorem.. and the bearing is 304 degrees 44 minutes and 55 secs.

Unknown008 · Jul 21, 2009, 01:34 AM

Yup for the distance, however, you made a mistake with the bearing.

It is 333 degrees 4 minutes and 35 secs.

You missed that point:

let F be the point where the boat is finally situated, O the origin point and I the intermediate point.

$<FOI = tan^{-1}(\frac{124}{86}) = 55.3$

let N be the North direction.

$<FON = 55.3 - 28'20 = 26.9$

$Bearing = 360 - 26.9 = 333'04"35.45$