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Problem 1Leni plans to use a ramp to make it easier to move a piano out of the back of his truck. The back of the truck is 33 inches tall and the ramp is 65 inches ...

Question

Problem 1Leni plans to use a ramp to make it easier to move a piano out of the back of his truck. The back of the truck is 33 inches tall and the ramp is 65 inches long. What is the horizontal distance from the end of the ramp to the back of the truck?Problem 2BongBong is admiring a statue in Seaside Park. The statue is 12 feet taller than he is, and BongBong is standing 16 feet away. How far is it from the top of the statue to BongBong's headProblem 3At ice-skating lessons, Manny attempts

Problem 1 Leni plans to use a ramp to make it easier to move a piano out of the back of his truck. The back of the truck is 33 inches tall and the ramp is 65 inches long. What is the horizontal distance from the end of the ramp to the back of the truck? Problem 2 BongBong is admiring a statue in Seaside Park. The statue is 12 feet taller than he is, and BongBong is standing 16 feet away. How far is it from the top of the statue to BongBong's head Problem 3 At ice-skating lessons, Manny attempts to do a complete revolution spin but only manages a quarter turn on her first attempt counterclockwise. What is the value of his first spin in degree angle? Problem 4 A rectangular football field is 64 meters wide and 100 meters long. Ping runs from one corner of the field in a diagonal line to the opposite corner. How far did the player run? Problem 5 The room thermostat was set to 22.034º C. Ronald wanted to set the temperature to 19.23º C. How many degrees’ cooler does he want it to be? Express your answer in minute-seconds


Answers

Solve each problem. See Examples $1-4$. A softball diamond is a square, $60.0 \mathrm{ft}$ on a side, with home plate and the three bases as vertices. The pitcher's position is 46.0 ft from home plate. Find the distance from the pitcher's position to each of the bases. (FIGURE CAN'T COPY).

In this course mm carries a figure which has given him because no. In Triangle angrily closed 90 degrees minus 35 which is 65 degrees. Now we will use low of sign language. Lady a year born Find Me equals uni upon time. 35 degrees. From here we'll find a equals. Two beauty 9 65 degrees, divided by sine 35 degrees It is given to us, which is attitude 5000 Quantifiable science, 55 degree divided by sine 35 degrees in solving it Bigger a 7900 points by now, again from Triangle E D. Angle, which delivery, Then we can find angles. Keep, which is 90 degree, minus 60 kind of spaced 30 degree. How we will use low of signs in Triangle ABC. Find the you're on sign. The degree equals a B Upon sci fi. There was a B science 60 degrees divided by a scientist Critically. Now the two villages 7900 point by science, 60 degrees divided by science degree. Thanks A people's to a is the perpendicular distance some airplanes don't today, you know you taken the value of a B equals to a 7900 0.5 multiplied by under three by two, divided by one vital holding. This good value of activities. 13,600 point. Mhm. Thank you.

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.

Yeah. In this exercise we know that Our five vehicles data and we want to solve for X. We know that tangent Harbaugh because 218 over x tangents are plus beta which is tangent to our for because 500 fifties real rounds enhance. According to this formula 553 over ads. He calls 218 Over X. Times two Divided by one miners 218 over x square first. We multiply both sides by X enhance this X is canceled. So one miners 218 over X squared. He calls two times 218 over 553 in the hands 218 x squared equals one Miner's 2 times 218 Over 553 and 218 Over X. He calls horns 46 enhance Eriks. He calls 400 73 points 943

Okay, so for this problem, we're going to have to use the law of co signs, which I have written this formula over here. And I have also drawn the diagram, so we know that each of the feet are sorry, each of the sides of the square or the diamond are 60 ft. These are all congruent and the distance from home plate to the pitcher's mound is 46 ft because it's a square. We also know that all of the angles are right angles, which means if I cut this in half, this is going to be 45 degrees. So that should give me enough information to find this side right here, which is the distance from the pitcher's mound to first base. My call outside A. Because I have angle A. Which is 45 and 60 ft, I'm gonna go ahead and label with B and 46 ft at sea. So I have a squared, which I don't know equals B squared, 60 squared A. C squared 46 squared minus two times 60 times 46 co sign of A. Which is 45. Now, you need to make sure that you are in degree mode for this problem and your calculator and not radiant mode or else your answer will come out incorrect and I had 60 squared it was 46 squared minus two times 60 times 46 co sign of 45 in my calculator. And that gives me for a squared 1812. Wait 77 I can and I'm gonna go ahead and take the square root of both sides to get A. And that gives me 42 0.588


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