1. DO NOW
For each problem, find the measure of x. Round to the nearest degree.

2. Do Now
Label opposite, adjacent, and hypotenuse for angle Z for the triangle below.
2. Find the ratios for Sin L, Cos L, and Tan L for the triangle below.
3.Find the missing side length for the triangle below.
4.Find the missing angle for the triangle below.

3. Meme of the Day

4. Special Right Triangles

5. What are we learning today?
Standard:
MCC9-12.G.SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Skills:
SWBAT build upon their previous knowledge of similar triangles and of the Pythagorean Theorem to determine the side length ratios in special right triangles.

6. Special Right Triangles
Make sure you are following along and copying down the notes on your own guided notes. Everything that is bolded and underlined should be copied down on your paper.
There are 2 types of special right triangles. One type of special right triangles is a triangle.

7. So what does 45-45-90 actually mean?
A triangle just means that that particular triangle has a 90 degree angle and 2 45 degree angles
But all triangles have a special pattern!
The legs of the triangle are equal in length, meaning that one leg is just as long as the other leg
The hypotenuse is √2 times the length of the leg

8. Special Right Triangles Video

9. leg x leg leg leg x x x x√2 x√2 hypotenuse hypotenuse
I Do: Ms. Massih will complete the following 2 problems. Make sure you have your pencils down, mouths closed, and eyes up at the board while she is doing the problem. You will have time to copy down the problem after I have finished the problem.
What is the value of each variable?
2. What is the value of each variable?
leg x
leg
Step 1: Label the legs and hypotenuse of our triangle
Remember: our hypotenuse is our side right across from the 90 degree angle
leg
leg
Step 1: Label the legs and hypotenuse of our triangle
Remember: our hypotenuse is our side right across from the 90 degree angle x x x
x√2
x√2
hypotenuse
hypotenuse
Step 2: Now label x, x, & x√2 on our triangle
Step 2: Now label x, x, & x√2 on our triangle
Step 3: Now think about which value we are solving for. In this problem, we want to find the length of the hypotenuse, right? We know that x=9 because the length of our legs is always 9, so what would the hypotenuse be?
Step 3: This problem is similar to Ex. 1, but this time our x has a radical. If we know that x=2√2, then what is the value of our hypotenuse?
Step 4: If we know x=2√2, then we would still multiply by √2 to get our hypotenuse.
What is 2√2 X √2?
Remember: √2 X √2 = √4= 2
So 2√2 X √2= 2 X 2=4
Therefore, x=4
Step 4: If we know x=9, then x√2 would be 9√2
h= 9√2

10. Let’s Do One Together!
What is the length of the hypotenuse of a triangle with a leg length of 5√3?
Step 1: Draw a right triangle.
hypotenuse
x√2 x
leg=5√2 x
leg=5√2
Step 2: Label your right triangle, meaning put in the angles you know, and label your legs and hypotenuse as x, x, and x√2.
Step 3: Now substitute in the values you know. 
Step 4: Solve for your variable.
If x=5√2, then x √2 would be 5√2 X √2
=5 X 2
=10
5√2 10
Step 5: Now write in all the sides for your triangle.
5√2

11. Got It?
Work quietly with your group members on the following 4 problems. We will review the answers as a class after. Remember, ask your group members before you ask the teacher!

12. Answers to Got It? Problems
1. y=60√2 2. y=√10 3. x=15 y=15 4. x=5√2

13. Triangles
Another type of special right triangle is a triangle.

14. Triangles
Just like triangles have sides as x, x, and x√2, triangles have x, x√3, and 2x.
Always try to start with the 30 degree angle the side across from that is x
The side across from the 60 degree angle x√3
The side across from the hypotenuse 2s

15. I Do: Ms. Massih will complete the following 2 problems
I Do: Ms. Massih will complete the following 2 problems. Make sure you have your pencils down, mouths closed, and eyes up at the board while she is doing the problem. You will have time to copy down the problem after I have finished the problem.
What is the value of d in simplest radical form?
x√3
Step 1: Label the triangle as x, x√3, and 2x x
Step 2: We know the side across from the 60 degree angle is x√3 and the length is 5. 2x
Step 3: If we know the side across from the 60 degree angle is 5, we can set it equal to x√3. Then we can solve!
x√3=5
√3 √3
X=5√3 3

16. I Do: Ms. Massih will complete the following 2 problems
I Do: Ms. Massih will complete the following 2 problems. Make sure you have your pencils down, mouths closed, and eyes up at the board while she is doing the problem. You will have time to copy down the problem after I have finished the problem.
What is the value of d in simplest radical form?
Step 1: Label the triangle as x, x√3, and 2x x
x√3
Step 2: We already solved for x in the previous problem, so we know that x= 5√3 3 2x
Step 3: If we are looking for f, we know it is the side across from the 90 degree angle, which is 2x.
2 X 5√3 3
Step 4: Now solve for the missing side.
f=2 X 5√3 = 10√3
3 3

17. Let’s Do One Together!
Find the value of each variable. If your answer is not an integer, express it in simplest radical form. 2x
Step 1: Label the right triangle above with the lengths for a triangle. (Ex: x, 2x, x√3) x
Step 2: Write an equation with the sides you are given.
If we know that the side across from the 90 angle is 40, we can set it equal to 2x.
2x=40
x√3
Step 3: Now solve for your variable.
2x=40
2 2
x=20
Step 4: Plug in the value of the variable and find the remaining 2 sides.
x=20
x√3=20√3
2x=40

18. Got It?
Work quietly with your group members on the following 4 problems. We will review the answers as a class after. Remember, ask your group members before you ask the teacher!

19. Answers to Got It? Problems
x=4
y=2
2. a=8√3

20. Independent Practice
Now work on the independent practice problems by yourself. Try to look over your notes and figure out the problem before asking your partner or the teacher for help!