So we have ah, diagram. And this gentlemen walked 800 ft, 800 ft. And then he turned and his angle well, kind of got that along here. He turned and went 43 degrees and he won a certain distance. And then he turned and he looked back. And now let's see if I could draw that to here. Why might actually touch it? It's pretty close. And this angle right here, when he turned and looked back, was supposed to be 29 degrees and in part a. We want to find How far did he walk in the off in the field. So we know if this angle is 43 degrees, we know that this angle is it Supplements 180 degrees minus 43 tells us that this angle is 137 degrees. And if we know that's 29 plus 29 the some of these two is 166. So 180 degrees minus 166. And that looks like 14. And this angle is 14 degrees. So we can set up with love signs to find side A. We know that the I'm gonna put the sides on top that a is to the sign of 14 degrees as this side, 800 ft is to the sign of its angle opposite, which is 29 degrees. And so if we take 800 times the sign so multiplying both sides by sign about 14 degrees, 800 times a sign of 14 degrees, make sure clothes off my parentheses, E and divided by the sine of 29 degrees Sign of 29. That tells me that at a distance is 399 point 20 ft. So almost 400 ft now on Part B, we wanna find how long this is. If he just turns around here and said, You know what? Let me just go straight back. So now we'll Dio be is to the sign of 137 degrees as 800 is to the sign of 29 degrees, and so we'll get what RB value is. And so we have 800 times the sign of 137 degrees, divided by the sine of 29 degrees, and that gives us 1125.39 ft. Now we want to figure out on part, see some time. So we know he walked, uh, 800 ft. We want to know, Is it fast for him just to go back? Or is it faster for him to retrace his route? So if he goes back, he's going to travel, Uh, five miles, 5 ft per second, 5 ft per second if he travels along the sidewalk, But in the field, he's only going to travel 3 ft per second. So let's let's figure out that part. That's easiest. If he travels 1125.39 ft and he travels at 3 ft per second, we need defeat to cancel out. So 3 ft per one second and now our feet will cancel and we'll find out how much time. So if I take that answer and basically divided by three, it will take him 375.13 seconds. If you just go straight back now, we're gonna have to figure out his speed. Uh, if we do both so he would go 800 ft on the sidewalk. 800 ft, but he travels 5 ft. Move that up just a little bit more. Her one second. Plus he's going to travel 399.2 ft and he's going to travel 3 ft in one second and that will cancel. My feet will cancel. So here we have 800 divided by five plus 399.2 point to type it in wrong, divided by three. And let's find out how much time that ISS this will take him. 293.7 seconds. So he needs to go back and retrace his route. He does not want to aim straight. It will take him longer. It takes him a lesser amount of time. If he goes back and retraces back along, whips back along here and back along there, that should be his route.