A ship sets out to sail to a point 149 km due north. An storm blows the ship to a point 121 km due east of its starting point. How far and what direction (as an angle from due east, where north of east is a positive angle) must it now sail ?

1 Answer

192Km at an angle 129.1 degrees from east


There are 2 parts to the question
1) How far should the ship sail
2) What is the angle it should take from the east direction

Part 1
The distance to be traveled is obtained by using Pythogoras formula
#a^2 + b^2 = c^2# as the given distances form the sides of a right angled triangle and the distance to be travelled forms the hypotenuse
so we have #c = (149^2 + 121^2)^0.5# i.e 191.94Km and approximately 192Km

Part 2
We effectively have to move west and north so we know that the angle will be greater than 90 degrees and less than 180 degrees from east
we also know that sine of the angle is #(149/192) = 0.776#
by taking the sin inverse, we get the angle = 50.9 degrees but we know it has to be between 90 and 180
so we use #sin(180-Theta) = sin(Theta)#
so the angle is 180 - 50.9 = 129.1 degrees from east