You drive 45 miles to Kingwood from Richmond at 30° North of East. Determine how far north and how far east you traveled. How would i answer this ?

22.5 miles due North

38.7 miles due East

Explanation:

From the information given above, we infer :

Let there be a vector AB (indicating distance travelled) with magnitude = 45 mi and makes an angle of 30° with East axis as well as an angle of 60° with North axis.

Displacement covered in North Direction :

AB Cos 60° = 22.5 miles due North

Displacement covered in East Direction :

AB Cos 30° = 38.7 miles due East

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west