All right. I try started this problem and I ran into some technical difficulty. Um So I'll go over what's done here so far. It says um what question are we all in here? Okay, so 12 newtons At 20°.. So this should be an end for Newton's. I drew this is 12 newtons here And I drew it at 20°.. And then on the end of it I drew 14 Newton's at 50 degrees. So 12 times the co sign, the co sign is going to be the adjacent, So 12 times the co sign of 20. And then in the Y direction it's going to be 12 times the sine of 20. And again, co sign as horizontal. Here sign is vertical. Okay then I just took these 12 co sign 20 plus 14. Co sign 50. Put it in a calculator and got 20.3. Then I took 12 signed 20 Because 14 sign 50. Put that in a calculator and got 14.8. Okay, so now we need to figure out magnitude and direction. So um I need to put back in 12 co sign of 20 plus 14. co sign of 50 12. Co sign of 20. Okay. Plus 14 Um co sign of 50. And that gives us the 20.3 and the 14.8 for the sign. Using the pythagorean theorem, I get a magnitude of 25.2 and then I get a direction using the inverse tangent of 36.2°.. Okay, now we move on to be. So I drew part B. Um Now 105° and let me erase some of what I've got up here so that maybe you can see better. There we go. I didn't want to raise that. Okay, notice that the second ray, the second vector Is 105°.. Well, 100 and five degrees is 90 plus 15. So after the 90° angle, then there's 15° more. So um 15 co sign of 15. 15 sign of 6, 15. But on the second vector um the we've switched the sign and the co sign because The Y direction is now the adjacent to 15° and the X direction is now opposite. So that gives me these and I could put them into Dismas. So that gives me 15 coastline of 15 -18 sign of 15. So that's going to give me 9.83 in the X. Direction. And that makes sense because it's positive. In the end it's going to be positive. And then I've got 15 sign of 15 fingers were in the wrong place. Um Plus 18 Co sign of 15. That gives me 16 62 Pythagorean theorem ends up being 19 And then the angle is 59°.. Now, that is not the same as what's written in Dez most. So I'm a non dez Mohsen enumerated. So I'm going to keep thinking about what I did here. 15 co sign of 15 is definitely what I wanted and that should be a positive number and it is. Then I subtract it off 18 sign and I got a smaller number. That makes sense to 12 sign of 15. 12 sign of 15. That should be a positive number, yep. And then this made it even more positive, positive and even more positive. So again, that's correct. Make sure that I'm in degree mode, which I am and then I did pythagorean theorem, which obviously is correct. Uh And then inverse tangent of V over a Y direction over X direction gives me this. So 19.3 at 59 0.4 degrees. Okay, let's move on to see, yeah, pick up the right pen here. 20 newtons at 3.13 degrees. Oh no, that's the answer. C20 newtons at 40° And then 15 newtons at 310°.. Okay, 20 newtons At 40°.. Let me try that again. Okay, Now 310° with 360 -310 is 50. So that would actually be at negative 50°.. So I'm going to start from up here, I'm going to go downward 50 degrees. And um this is 15 Newton. Okay, so uh again looking at components, we've got 20 Co sign of 40, We've got 20 sign of 40. And then we want to add uh 15. The X direction is the co sign of 50. 15. Co sign of 50. Um But then in the Y direction it's negative negative 15 signed of 50. So if I add those together in Dez mose I get 20. co sign 40 Plus 15. co sign 50. 20 signed, 40 -15. Sign 50. Okay, That gives me 25 newtons and three degrees, which is indicated as the correct answer. So thank you for watching.