Question

a boat sails 50km on the bearing 54 degrees . how far is the boat north of its starting point ?

Answer 1

I think for this one you need to drive in your COSy CAH

Use this formula triangle to find that
/ Adjacent \
/COS * Hypotenuse \

Adjacent = COS * Hypotenuse
COS = Adjacent/Hypotenuse
Hypotenuse=Adjacent/COS

Note the position of the variables in the triangle, and how adjacent is above COS and Hypotenuse, it tells you how to structure your formula for each result.

In this case you want to know the length of the adjacent side relative to your angle via COS

So the formula you want is Adjacent = COS * Hypotenuse
Plug in the numbers
Adjacent = COS[Angle] * Hypotenuse
Adjacent = COS[54] * 50

Answer 2

Remember the 3 acronyms, CAH TOA SOH, these create 3 formula triangles where the middle letter is ALWAYS on top of divisions, and if you want to find the value of the middle letter when you know the other two, then the formula is ALWAYS multiplication.

A
COSy CAH = C*H The Cozy Car

C = A/H
A = A*C
H = A/C

O
TAN TOA = T*A TAN'd Toes

T=O/A
O=T*A
A=O/T
O
SIN SOH = S*H SIN'g SEW'r

S=O/H
O=S*H
H=O/S

You can use this to easily work out if you need to divide or multiply the terms and nail your trig class.