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13) Solve: Round your answers to the nearest tenths(20 points) Regan throws a baseball 23.8 ft to Emma at a bearing of 2139 Emma then throws the baseball 10.9 ft to...

Question

13) Solve: Round your answers to the nearest tenths(20 points) Regan throws a baseball 23.8 ft to Emma at a bearing of 2139 Emma then throws the baseball 10.9 ft to Kaylie at a bearing of 1109 How far must Kaylie throw the ball back to Regan? What is the bearing from Regan to Kaylie?

13) Solve: Round your answers to the nearest tenths (20 points) Regan throws a baseball 23.8 ft to Emma at a bearing of 2139 Emma then throws the baseball 10.9 ft to Kaylie at a bearing of 1109 How far must Kaylie throw the ball back to Regan? What is the bearing from Regan to Kaylie?



Answers

Solve each problem. A plane flies $1.3 \mathrm{hr}$ at 110 mph on a bearing of $38^{\circ} .$ It then turns and flies 1.5 hr at the same speed on a bearing of $128^{\circ} .$ How far is the plane from its starting point?

Here. We have a 13 foot ladder. Um, that it Lee against the house in the distance from the bottom of the ladder to the house is seven feet less in the distance, in the top of the ladder to the ground. So here we let, um, the lanes of the two sides here are well, X and X, minus seven in the length of the high pot. News is, well, 13 feet, right? So, um, by the degree in serum, when we get here is a triangle it right triangle. And we know that, um well, X squared plus X minus seven squared well, must be equal to 13 square. So we have while x squared. Plus, we square our X minus 7 10 X minus seven. We get X squared minus 14 x. Ah, plus 49 right Is equal to 13 squared, which is 100 and 69. So, um, send this equals zero. We get well, two X squared right expert plus expert is two x squared, and then we have while minus 14 axe and it's attract over the 1 69 So we get minus 120 is equal to zero um Well, we can do here and make numbers a little bit smaller, right? Everything is even. We have even coefficients everywhere. You go ahead and divide everything by two to get X squared. Minus seven. X minus 60 is equal to zero. Okay, um, for now we have a quadratic instead of form, um zero. Right? So we can go ahead, and we can use the quadratic formula here to solve for X. So we know that X is equal to, well, negative B plus or minus the square root of peace equipment. Its for a c all divided by to wait so X is equal to or negative. Be so. Here be is, um, native 73 a minus, minus seven or a positive seven, plus or minus the square root of B square. So negative seven squared minus four times a, which is just one time. See, which is negative. 60 all divided by two a. So right about you. There's one. There's two. So therefore we have that X is equal to well, seven plus or minus. This becomes our 17 over to. Okay, well, the distance here. We're right. We're trying to find a distance and distance must be positive. Didn't go ahead and throw out the negative value here. Just care about what seven plus 17 is, um 17 18 1920.1, French 20 24/2, which is 12. Right. We can throw out the seven minus 17 myself. Seven minus 17 over to is gonna be negative. And again, this is a distance, which must be which must be positive. So therefore, we have that X is equal to, um, Trump. Okay, So, um, rest for the distance of the bottom of the ladder from the house is well X minus seven, which is equal to well, 12 97 which is equal to five. So we have five feet, right?

We have three towns mentioned in this problem. First, there's town A, and the other towns are measured at Barings from it. So let's put in a first tell me be is 26 miles from town A at a bearing of south 15 degrees west. So if I were to draw a north south east west system, if I started at the south axis and rotated 15 degrees toward the West like so they went 26 miles, I would get to town, be town, See. Meanwhile, is that a bearing of South seven degrees east? So I'm gonna start at the South axis and go seven degrees toward the east, which would put it right here. And if I traveled, it tells me 54 miles, so it's not to scale, but that's okay. 54 miles I get to town. See, we want to figure out the distance between towns, be and see which is here in black. Now, since this is a, I will say that that's angle a side. A is here. In fact, we can determine angle A because that's just the sum of the two angles that make it up. So angle a is gonna be 22 degrees. We can use the law of co signs to figure out a which is the distance between town be in town. See a squared equals B squared plus C squared minus twice bc co sign of a So that's going to be 54 squared plus 26 squared minus two times 54 times 26 times the co sign of 22 degrees. That will give us an answer of 988.5. And if we take the square root of that, we get A which again is the distance from B to C and to the nearest mile that is 31.

In this lesson board find the distance that is between the starting point of the endpoint of flight. So let's start by drawing the whole thing so that we can find the distance now. The plane started oh yeah On the barren of 38°.. Okay. And the mood for 1.5 hours with a speed off 110 mph. So this translates 243 miles. Okay. Then it moved. Uh the bearing of yeah 128 Degrees. 228 90 is covered here Then 38 is covered there. Okay So it moved for 1.5 hours Then at the speed of 100 10 mph. So that makes it 106 165 mi. Okay? At this point this is the this is the the ending point. So we have a baby. Oh and see. Yes. So what we'll do is that we joined the two points then you find the distance A. C. So here I've had the alternative to this and that is 62°.. So 28 Uh 30 just taken their 60 just sticking 62 2nd here. So that makes the whole thing here 90 The 90 faces this side. Okay. So in order to find a C. Find it as the yeah, the squared of a C. Is equal to the sum of squares of the sum of squares of the other two sides. Yeah, so a C squared, it comes 143 squared plus 165 squared. So a C squared becomes 47674 and a C. Becomes the square root of this number. Mhm. So AC. The length of that as opposed merely 218 mi. Okay, so it means that the distance between the starting point and the ending point As 218 mi. Thanks for time. That's the end of the last. Cool. Yeah.

We have 64 number problem in which a person in a plane flying a straighten out observes a mountain at the bidding of 24.1 degree. At the time the plane was it 7.9 took along address on the mountain. OK, so time later, the bearing to the mountain becomes archaeologists say he started from point A and mounting was here. So the bidding waas because the building should I will always be with north direction. Oh, I suppose the bidding lettuce Just wonderful 0.1 degrees. So little stride toe this to be a 24.1 degree, 24.1 degree. So at this time, this is 7.92 kilometer it is given. No. After some time the bidding becomes 30 to 1 70. So let us say plan, which is here That won't be. And now the bidding chicken is this Is this really the bidding from being taken? Will be 32.7 degree, so we need to find the value off if we ah, let this see. So we need to find the value of B C. Okay, so this is 32.7 degree 32.7 degree. Okay, Okay. Okay. So and girl, ABC will be cool toe 180 degree miners were talking about this angle. One of the TV miners 32.7 degree, which will vehicle to 147.3 degree five months, 37 months before. Okay, 147 degree. Now we will be a playing. Yeah, signed law because the angle and the side oppose it to this angle is given. So a sign. 147.3 degree divided by a C that is 7.92 equal to sigh in 24.1 degree over BC. So from here BC will be equal toe B c will be equal toe 7.92 Do sign a 24.1 degree divided by science 147.3 degree when you need to use Calculated 7.92 into a sign before san trimmed to 4.1 degree. Do right by a sign 147.3 Sigh plant 9861 So when the beating world tear it open seven degree the distance bc waas approximately five point nine nine kilometers. So this is the Hans. Thank you so much


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