Unit 8 right triangles and trigonometry homework 2 special right triangles

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Geometry

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'Unit 8: Right Triangles & Trigonometry Homework 2: Special Right Triangles...Please Help! 16. 16,6 45 30'

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I am a given preliminary to find out for X, Y and Z. Right? So for that some of the problem here. But before that let's learn some basic concepts. Here's soybean hard riding a triangle straw here, Riding rangel Automatic ratio. This is 90 is this T dog here the first I actually think this is uphold it is stable and his. Right. So we have science theater is equal to oppose it overhyped Dennis the worst thing to do adjacent over hypotenuse and then theater they called to oppose it over at justice. So that's what we're going to use the cinematic ratios to find out the solution for the given problem. We've got a strangle here struggling to see so why not X. Right. So where do you apply applies here to go for saying do you do You go four years time theatre sign 30 Right 7 30 Let's oppose it. That is acts over Exchange three happiness right then that is 1/2 or they will do acts over exchange fruit trees are from here we get Act is going to be equal to eight trees 823 Let me have gone. I wonder why and see we need this this length here. We need to hear this length. Right? So for that I'm going to use here now on same triangle what I'm going to use I use no cause 30 so costs are equal to adjustments. So I understand doctor this is Cuban else here maybe so maybe it isn't. So a B Over we have happiness. That's 16 route three External routes of course 30 has given us root 3/2. That is equal to a b. over 16 road treat assaulting the swinger. A. B. Is equal to 16 route three time through three. Right? All divided by two. Yes General three times so three all divided by two. That's gonna have to be 24. So 24 here, this is 24. The next part is I want to find out why. And the right at this angle is 45. You know that the angles and property for triangle is 180 those 45. So the single would also be 45 because we have 45 plus 45 is 90 plus 90 is 1 80. I'm again debating $9 in property we have used here. This is 45 45 to 45 plus 45 90 19 nineties when it was 45. So now we know that though in this triangle abc let's say and the strangle we have so the two angles are equal in the sight of a positive. That will be equal. This will be why this will be equal to Y only. So it will be why? That's also why? So we have the C. Is equal to Y. And what's the next champ in solving this? So in crime of abc we want to use the pythagorean triangle. Abc we're going to use the despite the gorgeous to europe. So if we use this term now will have wide square, right? The white square plus y squared Not equals 24 square. If you use that Soul two White Square e Quilts 24 sq. So You start twice for equals 24 times 24. Forward to So 12 here. So I will get Y squared equals 12 times 24. So if I just backed priceless, so y squared is equal to Well is two times 2 times three Times 24 is two times 2 times two times 3. Right? So what we get here, why is coming up to me to make a pair too? Times true times three. And then Route two. So Why is coming up to me to have a route to? So why is well road to? That means these also coming out to be 12 to So I and D. What are coming out to be Well, rule two. Thank you.

Presentation on theme: "Chapter 8: Right Triangles & Trigonometry 8.2 Special Right Triangles."— Presentation transcript:

1 Chapter 8: Right Triangles & Trigonometry 8.2 Special Right Triangles

2 Isosceles Right Triangles What are the angle measures of an isosceles right triangle?

3 Theorem 8-5 45-45-90 Triangle Theorem –In a 45-45-90 triangle, both legs are congruent and the length of the hypotenuse is √2 times the length of a leg

4 Example 1 Find the value of h:

5 Example 1 Find the value of x:

6 Example 1a Find the length of the hypotenuse of a 45- 45-90 triangle with legs of length 5√3.

7 Example 2 What is the value of x?

8 Example 3 A high school softball diamond is a square. The distance from base to base is 60 feet. To the nearest foot, how far does a catcher throw the ball from home plate to second base?

9 Example 3a A square garden has sides 100 ft long. You want to build a brick path along a diagonal of the square. How long will the path be?

10 Theorem 8-6 30-60-90 Triangle Theorem –In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is √3 times the length of the shorter leg.

11 Example 4 Find the value of each variable:

12 Example 4a Find the value of each variable:

13 Homework p. 428 1-6, 9-14, 17-22