A ship sails N 27°10' E for 39 km and then turns N 67°50' for 85 km. What isad the distance and the bearing of the ship from the starting point?

>>>So, I have a sketch of one triangle(not a right triangle, then drew 3 right triangles all over it then solved for their sides and angles..

I came with a distance of 90.38 km, a bearing which is N 47.63° W. Did I got them right?

I assumed that by N 67°50' , you meant

N 67°50' W
I had a triangle with sides 85 and 39 and the angle between them as exactly 85°
Using the cosine law I got your distance.
Good job

now look at the actual triangle.
let the angle at the bottom be Ø
so sinØ/85 = sin85/90.38
sinØ = .93689...
Ø = 69.536 , but that includes our original 27° 10'

so our bearing will be 69.536° - 27°10'
= 69°32' - 27°10'
= 42° 22'

or N 42°22' W

Here is a little hint:
using your D°M'S key on your calculator you can actually perform all arithmetic calculations in the degree-minute-second notation
Play around with it a bit to become familiar with it.
So unfortunate that degree measurements and time measurements are not metric.

To verify if your calculations are correct, let's calculate the distance and bearing step by step:

1. Converting the angles to decimal degrees:

N 27°10' E = 27 + (10/60) = 27.167°
N 67°50' = 67 + (50/60) = 67.833°

2. Using the given distances and angles, we can determine the coordinates for each point:

Starting point: (0, 0)
Point 1: (39 km * sin(27.167°), 39 km * cos(27.167°))
Point 2: (39 km * sin(67.833°), 39 km * cos(67.833°))

3. Calculating the coordinates:

Point 1: (17.68 km, 33.24 km)
Point 2: (35.49 km, 74.61 km)

4. Using these coordinates, we can calculate the distance between the starting point and the final point using the Pythagorean theorem:

distance = sqrt((35.49 km)^2 + (33.24 km)^2) ≈ 47.61 km

5. To find the bearing, we can use the inverse tangent function and convert the result to the correct format:

bearing = atan((35.49 km) / (33.24 km)) ≈ 47.63°

Since the bearing is positive, it would be N 47.63° E (not W).

Therefore, the correct calculations are:

- Distance: Approximately 47.61 km
- Bearing: N 47.63° E

It seems that your distance calculation is slightly off, but your bearing is correct.