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Question 2Which of the following set of lengths forms an acute_trianglez0 1,340 3,4.5J0 4 4,,610 5,6,7...

Question

Question 2Which of the following set of lengths forms an acute_trianglez0 1,340 3,4.5J0 4 4,,610 5,6,7

Question 2 Which of the following set of lengths forms an acute_trianglez 0 1,34 0 3,4.5 J0 4 4,,61 0 5,6,7



Answers

In Exercises 37-40, find the lengths of the sides of the right triangle with the indicated vertices. Show that these lengths satisfy the Pythagorean Theorem.

$(2, -1, 2), \quad (-4, 4, 1), \quad (-2, 5, 0)$

Number 30. They want side length D A. We're just going to use Pythagorean theorem. Okay, The side across from the right angle is the high pot news that is always side length C. Okay. And for the other two sides doesn't matter which is a and which is B. So I'm gonna make 16 side length be. I'm gonna make d a side length. A Pythagorean theorem is a squared. Plus B squared equals C squared. A squared is what we're looking for. B squared to 16 squared and C squared is 20 squared. A squared is still there. B squared is to 56. 20 square is 400 and we just subtract to 56 from both sides. Okay, this cancels right here to 56 minus 2 56 and we're left with a squared equals 1 44 Okay, take the square root of both sides, and the square root of 1 44 is just 12. And we said a waas segment D a. So that's just 12. Okay, quick, Short cut. I can show you. Um, the most common right triangle. The sidelights are three, four and five. Okay. Where five is your high pot news. Okay, so if you make this side five in order to get 20 we do five times four. Okay. In order to get 16 we do four times for Okay, So for side length A, we can say it will be three times for which is 12. Okay, so basically, you have You have a three, you have a four and you have a five. And you multiply each side length, each one of those by four to get another right triangle. So that could be a short cut you use if you remember that 34 and five are the side lengths of a right triangle and you multiply all three by the same number.

Mhm. Let us take the right angle. The shortest side. S. E. Next big side. There's a publicity and the hypotenuse as the longest which is able to study is in the particles term. I can say that a plus two D. Square will be equal to D. Plus D. Square plus years square. This is nothing but a square plus 40 square plus for a D. Should be equal to a square plus D. Square Plus two a. d. plus. Do you square When you square gets canceled? We are left with a square minus three D. Squared minus to a D. Equals to zero scan Britain. S. E square minus 3 80 plus 18 -3 Day Square equals to zero. Taking a common. This is the minus Cd plus the T -3 D. Equals to zero. So we get either a testy A -3 D equals to zero. Which means that either a plus the zero or a men's three D. Zero. A place it is one of the sites so it cannot be zero. So let's take a men's three days zero from where we get equals to three D. Which means that A has to be a multiple of three. The shortest side is a and it has to be a multiple of three. The only option which is a multiple of three, is option three, Which is 1, 2, 7, 5. Not so.

So for this question, they want us Thio. Find the link subsides of the right triangle with the indicated Vergis is all right now. 002 They're ah or zero negative to five to get. So they claim these of the reddest cities for a triangle in particular, it's a right triangle, and they wanted to verify link, satisfy with jaggery and so a good additional exercise. It's the drop. How this triangle is embedded in three dimensional space. That's extra. We can actually just use algebra to verify that it is a right triangle that we do that well. We have three points, right? They were deceived. How do I compute the distance between each of them? We can use our three dimensional distance formula, the one where distances movie the square of these x accordance attract each other, plus the white corn in cities attract each other. What for? It's quiet. Let's see the track's era to square. Okay, so this is the length of one of the sides. This is the distance between two bird disease. How do I find another one? Well, I just think to other point. Let's finish competing. This one. This will be 16. That's so before. So this is scary of 20 one of it. Okay, irrational number. That's fine. Let's compute the length of another side. So we move on to more braces. Well, have there Ah, track to such as squared, plus the difference of their Y coordinates. And then I'll square them. But one's word. One square, you square it. It's the same thing. So now Z coordinates zero minus two negative. Two squared and we end up with three emotional distance of four plus one. That's for its name. No, that's computer final link. Offside this vertex to this protect notice. We're essentially drawing a line like and their heads of this distance between these points every time we compute it. So from this point, let's say, from seat two now compete that distance negative to subtract. Zero squared. Now, let's truck there. Why? Court admits for me, Charlie. Five track zero squared And then two years of track. Two squares. Yeah. What do we end up with? We end up with 4 25 29 Thank you. Let's verify that these all satisfy the, um, thuggery. And they're, um Well, what? As long as I'd have to be. Bye bye. Well, this one's going to be squared of 29. Squared is equal to the other two sides. So the square root of 20 square lost square root of nine squared and it does indeed look like it satisfies the thuggery and serum 29. But that is definitely 29. Awesome under it. Who?

Okay. Number 32. They want us to find B R. Okay. We already have B I Which is this side length here? 25. And we said in the previous problem, IR is 15. Okay, so be our equals. B I minus r I br equals b. I minus r, I okay. And we know that we know that B I is 25. Okay, that was given. And we know that I r is 15. So that's just 25 minus 15 and that equals 10.


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