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0f 7 (1 complete)Hw Scoro: 14,2934,1 0/7 pS13.9Queslion HcpSoive Ihe triangle(Fautducimm uucuntcucu )...

Question

0f 7 (1 complete)Hw Scoro: 14,2934,1 0/7 pS13.9Queslion HcpSoive Ihe triangle(Fautducimm uucuntcucu )

0f 7 (1 complete) Hw Scoro: 14,2934,1 0/7 pS 13.9 Queslion Hcp Soive Ihe triangle (Faut ducimm uucu ntcucu )



Answers

$7-8$ Find the lengths of the sides of the triangle $P Q R .$ Is it a right
triangle? Is it an isosceles triangle?
$$P(3,-2,-3), \quad Q(7,0,1), \quad R(1,2,1)$$

Our first step in this problem is going to be plotting our points of a triangle so we can start with point D, Which is that Negative seven negative one. Oh, which is going to be right here? Next we have point E, which is that negative one negative one. I'm right here. And lastly, we have point F which is negative seven negative nine, which is going to be all the way down here. And so from here we can go ahead and connect our points to figure out what our triangle should look like. Essentially, we're just going to find the perpendicular by sector of two of our sides. And from there we're going to be able Thio address determined where they intersect, which is where our circumstantial will be. So because we can see that the slope of side D all right here is going to be a slope of zero and the slope of side D f is going to need undefined now that's going to tell us that it's going to be much easier to finally perpendicular by sectors of these two sides so we can go ahead and start by finding the midpoint of side d e. So we know that the midpoint formula is going to be given to us by the average of the X values. So that'll be negative seven minus one over two and then the white corn. It will be the average of the Y values. And so once we end up solving this, we're going to find that our midpoint of these points is going to be a negative for, um, negative one. So are mint point for a d. E. A. 70 eat is going to be a negative for negative one. So from here, we're going to be able to write the equation of are perpendicular by sector. So, like we said, we know that means to have a slope are an undefined slope. So that means that since our X coordinate here is negative for our equation for the perpendicular by sector of side D is just X is equal to negative for And so finally, we're going to find the equation of the perpendicular by sector of side D. So again, our main point is the average of the two X coordinates, or casino de but a D f. So our X coordinates are going to be negative. Seven plus negative seven divided by two. And our why Cornet will be negative One last negative night and divided by two So are mingling with me Simplify. It is going to just be a negative seven for our X coordinate and then our y cornet will be made to five. And so like we said, since side D f is just a vertical line, that means that are perpendicular by sector is going to be a horizontal line. So in other words, we can just write this as y is equal to negative five and from here we can see that the points where they're going to intersect is where our X coordinate is going to be negative for in our white corn it is going to be negative five. So the coordinates of our circumstance er is at negative for

We're going to do problem number. And in discussion, we are possessed to prove that they were points which are given are the points of right triangle. So the point is 1:04. Now writing the another point Going to be that is a 6:00 -4. Letting the another point see that is a -15:00 -6. When the Supreme Government a 6-year business trade this 15 clearly -13 Government six. Now. Fine. So let's just find this law for slope. We are going to use the formula that is Y. 2 -5 on by X. Too many sexual. Finding the slope of a. b. 1st. So putting the values uh Y. To the value of to heaven. An extra action. So how do I do is manage store? Why? one is 4 By X two. X 2 is six. X 1 is one. So this will give us Menace eight x 5. The slow path. Amy now finding the slope of BC. So uh Why do his men 6? When when his men is four By X two is minutes 15. Our next one is 6. So this is giving us minus six plus four minus six plus four is managed to By -15 -6. So this is managed 21. So that's Lopez two x 21. Okay, the slow best. Goodbye. Thank you. No, we are going to find the slope for a C. So same formula. So why to his menace six weapon is -4 Extra Extra is -15. Our next one is -1. So this is coming out to the madness 10 x -16. So management's will get cancelled out. And if you just Divide never done element by two. So the swimming or not to be five x 8. So we got this slope now slope of all these three that as many as eight x 5 comma to buy 21 comma five x 8. Now, As we can see this and this to the product is giving -1, which simply means that they are perpendicular to each other. So what happens in right angle triangle is one side is will be particular to another side. So this will without a particular one. Okay, So this will be the answer. Thank you.

So we want to solve this triangle. We know that Angle α or Angle A. is 73° Angle beta is 28°. And we know side C is equal to 42 ft. And so let's draw let's say that's 73° roughly. And let's say that thing will bait and say that's about 28. So let's say this is alpha, this is beta. And again we're told that this is 73 degrees and this is 28 degrees. This would be side B. This would be side little A. This will be a big angle. See And this side C is given to us as 42 ft. So we don't know this angle but we can find that ankle because we know the measure of that is going to be that 180°. Type it in my calculator, less than 73, less than 28. Last 73 less 28. And so that angle is 79°. And so now we know this angle is 79° and we have a side angle pair and we want to find these two sides. So we're going to say a. Is to the sign of its angle opposite because we can put the sides on top or the angles on top that's up to us As 42 ft is to the sign of 79°. And then if we multiply 42 Times The Sine of 73, make sure your calculator is in degree mode and divided by the sine of 79°. We find out that that measure of a is 40 point. Let's see approximately nine sq feet, husband just sneezed. Now we want to find side B. O. And one by the way, 79 degrees is larger than 73 but not a lot larger. And notice that side A. Is smaller but not a lot smaller than side seat. That's something just to look at. Now we anticipate this side being much shorter because this angle is much smaller. So we know that B is to the sign of 28°. As and use what was given As 42 ft is to the sign of 79°. So again, we can find b by taking 42 Times The sine of 28° And then dividing it by the sign of 79, just doing a little bit of algebra And notice how much smaller that side is. This would round off to 20.1 ft because about to be 20.086, which were ground again to the .1. So that is our situation. We found this angle, We found that side and that side we are all solved

And this problem, we've been given three verjus is here we have a is at 14 B. Is at 6 92 4. And then see is that negative 15, negative six. And we want to show that there is a right triangle. Now, in order for it to be a right triangle, that means that we need to have two of the sides be perpendicular one another. And so in order for two of the size of the perpendicular to one another, we need to deal with their slopes. So that's what we're going to deal with. Here. We are going to deal with their slopes. And so let's begin with a slope of side A. B. So just take the points A. B. And find the salt between them. So this is four minus than heretofore over one minus six, which is 8/90 to 5. And so it has a slope of negative 8/5 into the line. Through A B. As a slope of negative 8/5. Yeah. Now let's look at A. N. C. Yeah. So for a C. Again finding ourselves, we have four minus negative six over one minus 92 15. Yeah. Which is 10/16, which is 5/8. And so notice that these are opposite reciprocal of one another. And so what that means that A. B. It's perpendicular to a. C. And so abc is a right trying.


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