# Thread: Spherical Trigonometry Help? (Trig with latitudes)

1. ## Spherical Trigonometry Help? (Trig with latitudes)

A ship travels from a point near Hawaii at 20° N latitude directly north to a point near Alaska at 56° N latitude.

a) Assuming the Earth to be a sphere of radius 4000 mi, find the actual distance traveled by te ship.

b) What fraction of the Earth's circumference did the ship travel?

I have no idea how or where to start on this problem. Can anyone help me? I read on this site that the degrees of a spherical triangle add up to more than 180°.. so I dunno how to begin the problem..

KryssTal : Spherical Trigonometry

The site also sows cosine and sine rules for spherical trig, but I don't see how I could use those since they don't give me much values in the problem to start with.

2. Originally Posted by toinfinity
A ship travels from a point near Hawaii at 20° N latitude directly north to a point near Alaska at 56° N latitude.

a) Assuming the Earth to be a sphere of radius 4000 mi, find the actual distance traveled by te ship.

b) What fraction of the Earth's circumference did the ship travel?

I have no idea how or where to start on this problem. Can anyone help me? I read on this site that the degrees of a spherical triangle add up to more than 180°.. so I dunno how to begin the problem..

KryssTal : Spherical Trigonometry

The site also sows cosine and sine rules for spherical trig, but I don't see how I could use those since they don't give me much values in the problem to start with.

a.

If you join the two places to the centre of the earth,
there is a 56-20=36 degree angle between them,
as the ship is sailing due north.

Hence you only need to calculate the length of arc of that line of longitude.

$\frac{36}{360}2{\pi}r=\frac{2{\pi}r}{10}$

where $r$ is the Earth's radius.

b.