Aroller coaster moves 85 m horizontally, then travels 45 m at an angle of 30.0° above the horizontal. what is it's displacement from its starting point?

There are 2 vectors representing the displacement: one is,  <85,0> and the horizontal and vertical components of the second, (45 cos 30.0 for horizontal) which is equivalent to 39m, and (45 sin 30.0 for the vertical) which is equivalent to 22.5 m. The components of the second vector therefore, is <39, 22.5>.  

  Therefore, the 2 vectors are:
1. <85,0>
2. <39, 22.5> 
 In adding 2 vectors together, follow this formula: <a1, a2> and <b1, b2>.
The sum of the two vectors is: <a1 + b1, a2 + b2>.

 Add:
<85 + 39, 0 + 22.5>

You will have the resultant vector for the displacement (not the actual displacement). If you want to get the actual displacement in meters, calculate the resultant vector: the square root of (a^2 + b^2) where a and b are the components of the resultant vector.

The answer is orbit around nucleus