Hello, tacubo!

I assume you made a sketch . . .

A roller coaster at an amusement park starts out on a level track 50.0 m long

and then goes up a 25.0-m incline at an angle of 30° to the horizontal.

It then goes down a 15.0-m ramp with an incline of 40° to the horizontal.

When the roller coaster has reached the bottom of the ramp,

what is its displacement from the starting point?

Code:

C Q
* - - - - +
* : * 40° :
25* : * :
* : 15* :
* : * :
* 30° : *
* - - - - - - - - * - - - - - + - - - - D
A 50 B P

The roller coaster starts at $\displaystyle A$, goes 50 m to $\displaystyle B.$

Then it goes up a 25-m incline at 30°.

In right triangle $\displaystyle CPB:\;CP = 25\sin30^o = 12.5,\;\;BP = 25\cos30^o = 21.65$

Then it goes down a 15-m incline at 40°.

In right triangle $\displaystyle CQD:\;QD = 15\sin40^o = 9.64,\;\;CQ = 15\cos40^o = 11.49$

Here is the diagram with the distances labelled. Code:

C 11.49 Q
* - - - - +
* : * :
* : * :9.64
* : * :
* :12.5 * :
* : *
* - - - - - - - - * - - - - - + - - - - D
A 50 B 21.65 P 11.49

Can you finish the problem now?