Here is the question:

A highway curve forms a section of a circle. A car goes around the curve. Its dashboard compass shows that the car is initially heading due east. After it travels 840 m, it is heading 35.0° south of east. Find the radius of curvature of its path.

[I'm wondering how to solve this problem if someone can show me step by step it would be a lot of help thanks in advance.]

[edited: Reading that it said I should show that I have at least attempted this OK,
well the question above isn't my homework assignment its just an example that I can use for a reference that I found in my text book
I tried using the suggestion my teacher gave me of s = r θ where θ is in radians, I though that 'S' would be 840 and the theta would be 38° but when I do the math my answer comes out wrong. Even if you don't give me the answer showing me how to solve it would be a great deal of help also thanks again.]

Your original problem states 35°, your attempted solution uses 38°. That could be part of the difficulty or a typo.

The s = r θ when a complete circle has been traversed becomes s = 2 * pi.

The suggestion your teacher gave is the way to go. You need to convert the compass heading from degrees to radians.

Did that help?