1. OBJ: To calculate the lengths of missing sides by using templates provided illustrating the 45-45-90 and the 30-60-90 right triangles.

2. 45-45-90 45 90 A 45-45-90 triangle is basically a square cut through its diagonal. The legs are the same length but the hypotenuse is about 1.4 times longer than the leg. Its size difference is represented by multiplying the leg by

3. LEG HYP Multiply the leg by √2. Simplify any and all radicals.

4. Example 1 Solve the following problems by following this simple rule: When going from a LEG to a HYP, multiply the leg value by √2. 45 90 A W R 1.AR=7. Find AW. 2.RW=23. Find AW. 3.AR=√10. Find AW. 4.AR=3√6. Find AW. 7√2 23√2 √20= 2√5 3√12= 6√3

5. Going from a leg to a hypotenuse is easy but it is a different situation when given a hypotenuse and you are trying to solve for a leg because DIVISION is involved. The next slide will provide you the rules you will need to successfully solve for any leg given the length of a hypotenuse.

6. HYP LEG When the hyp is an even radical, -divide the hyp by the √2. When rule #1 does not apply, -divide the hyp by 2 -then tack on (multiply) by √2

7. 45 90 A KR Example 2 1.AR=√30. Find AK. 2.AR=√46. Find KR. 3.AR=3√6. Find KR. 4.AR=12. Find KR. 5. AR=30. Find KR. 6. AR=6√7. Find AK. 7. AR=8√5. Find KR. 8. AR=5√2. Find AK. 1.√15 2. √23 3. 3√3 4. 6√2 5. 15√2 6. 3√14 7. 4√10 8. 5

8. 30-60-90 30 60 x 2x x√3 In a 30-60-90 right triangle, the shortest leg is labeled as an “x”. The hypotenuse is twice as long as the shorter leg so it is labeled as a “2x”. The longer leg is about 1.7 times longer than the shorter leg so it is labeled “x√3”.

9. Example 1 9030 60 5

10. Example 2 9030 60 12

11. Example 3 9030 60 2√5

12. Example 4 9030 60 4√3

13. Example 5 9030 60 12

14. Example 6 30 6090 16√2

15. The tricky part is when a number is given on the longer (x√3) side. When that is the case, we follow similar rules as we did with the 45-45-90 triangle. On the x√3 side, If the given number is divisible by √3, then simply divide by √3. If the above rule doesn’t apply, then: -divide by 3 -then tack on (multiply) by √3.

16. Example 7 30 6090 √30

17. Example 8 30 6090 6√3

18. Example 9 30 6090 12

19. Example 10 30 6090 14√6

20. Example 11 30 6090 33

21. Example 12 (honors) 90 45 30 24 A RD T Find the length of DT.

22. Example 13 (AP) 90