1. Right  s and trigonometry 7 Pythagorean Theorem the determine right triangles 6 Pythagorean Theorem, solve sides 5 WP: Pythagorean Theorem 4 Special Right Triangles 3 Sine, Cosine and Tangent ratios 2 Trig to solve sides in a  1 WP: Trigonometry Unit Review

2. 7 Pythagorean Theorem to determine right triangle What is the proper pronunciation for the second day of the week? a) T EE - USE - DAY b ) C HOOSE-DAY c) T WOS-DAY d) None of the above

3. 7a Pythagorean Theorem to determine right triangle If the Pythagorean theorem works for 3 numbers (“c” will always be the largest), then these values form a right triangle. If a 2 +b 2 =c 2 is true, then it is a right triangle Keep in mind that C will ALWAYS be the longest side

4. 7b Pythagorean Theorem to determine right triangle Ex1. How many of the triples below could be sides of a right triangle? (14, 48, 49) (33, 56, 65) (9, 41, 40) (45, 36, 27)

5. 7c Pythagorean Theorem to determine right triangle Ex2. Which of the triangles described in the table is a right triangle? Side 1 Side 2 Side 3 Triangle Q10 8 6 Triangle R11 8 19 Triangle S10 8164 Triangle T1101110

6. 6 Pythagorean theorem A Whip!

7. 6a Pythagorean theorem Remember this….. a 2 +b 2 =c 2 What does the letter “c” represent? __________Hypotenuse What does “a” and “b” represent? _______________ The legs of the  This only applies to right triangles! _ _ The side opposite the right angle is the __________ Hypotenuse c hypotenuse

8. 6b Pythagorean theorem 10 8 Ex1. Find the missing side of the triangle 8 2 +10 2 =h 2 From Pyth theorem 64+100= h 2 Solve 164= h 2 Ex2.  ABC is a right triangle with hypotenuse c and legs of length a and b. If b = 8 and c  10, then a = _____. 10 8 a

9. 5 WP: Pythagorean theorem Imagine a bridge that spans a canyon of two miles. (5280 feet = 1 mile) 2 mile bridge Unfortunately they forgot to place expansion joints into the bridge and when it gets hot, the bridge expands exactly one foot. How high does the bridge bow upward with this expansion? 2 mi + 1 foot bridge What is the height? (Approx)

10. 5a WP: Pythagorean theorem Draw a picture and label it!!!! The city commission wants to construct a new street that connects Main Street and North Boulevard as shown in the diagram below. The construction cost has been estimated at $100 per linear foot. Find the estimated cost for constructing the street. (New Street) Main St. N. Blvd 3 mi. 8 mi. 8 2 +3 2 =c 2 64+9=c 2 73=c 2  73=c The new road is  73 mi. (  73)(5280) (x) by feet/mi. (45112.339)($100) $4,511,233.90 Approx

11. 5b WP: Pythagorean theorem Ex2. Janina used the diagram to compute the distance from Ferris to Dunlap to Butte. How much shorter is the distance directly from Ferris to Butte than the distance Janina found? 20 mi 21 mi Ferris DunlapButte ?

12. 4 Special Right Triangles Do you have a calculator with Sin, Cos & Tan buttons?

13. 4a 45-45-90 Triangles || = What are the degree measures of this  ? 45° If we had a leg length of 1, what is the hypotenuse? (Use Pythagorean theorem) _______ 1 1212 If we had a leg length of 10, what is the hypotenuse? ______ 0 10  2 Using the Pythagorean theorem we can conclude: P P || = P2P2 For all 45-45-90  s

14. 4b 30-60-90 Triangles 60° 30° 5 10 w Using the Pythagorean theorem, find “w”! NOW!!! 5 2 +w 2 =10 2 25+w 2 =100 w 2 =75 w=  75  75 / \  25  3 5353 5353 60° Using the Pythagorean theorem, we can conclude: P 2P P3P3 For all 30-60-90 triangles

15. 4c 45-45-90 Triangles Ex1. In  ABC,  A is a right angle and m  B=45°. If AB=36 feet, find BC. A B C 45° 36 ft BC=36  2

16. 4d 30-60-90 Triangles 30° 60° P 2P P3P3 Ex2. In a 30-60-90 triangle, the hypotenuse is 28 feet, What is the shorter leg? ___________14 feet What is the longer leg? ___________ 14  3 28 14

17. 3 Sine, Cosine & Tangent ratios Bible trivia time……. How many years did Moses wonder the desert before he entered the promised land? Moses reached the promised land, however, God forbade him entrance. How many wise men went to see Jesus? We don’t know, we only know of the mention of three gifts. 25 point reward for turning in calculators that are missing from my class…!

18. 3a Sine, Cosine & Tangent ratios S ome O ld H ippie, C ame A H opping, T hrough O ur A lley SCTSCT ine os an= == Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent Remember this and you will have it easy…! Adjacent - The leg touching the angle Opposite - Leg opposite the angle Hypotenuse - Side opposite the right angle

19. 3b Sine, Cosine & Tangent ratios A BC 9 1215 Is this a right  ? _________ yes Why? _______________Since a 2 +b 2 = c 2 What is the Sine of  A? ___________ 9/15 = 3/5 What is the Cos of  A? ___________ 12/15 = 4/5 What is the Tan of  A? ___________ 9/12 = 3/4 SCTSCT OAOHHAOAOHHA

20. 3c Sine, Cosine & Tangent ratios

21. 3d Sine, Cosine & Tangent ratios

22. 2 Trig to solve sides in a  I am thinking of two common objects, they both carry out the same function, but one has thousands of moving parts and the other has no moving parts. What are these items? Hurry, times a wasting….!

23. 2a Trig to solve sides in a  Remember 27° 7 x Solve for x. Which side are we looking for? a o h Which side do we have? a o h Since Cos uses “a” and “h”, we are going to use the Cos function Cos27= 7x7x (cos27) (x)= 7 Cross Mulitply  x  7.86 PS.  means approx equal SCTSCT OAOHHAOAOHHA

24. 2b Trig to solve sides in a  25° 7 x Solve for x What sides are we working with in reference to the angle?O & A Tan25= X7X7 (Tan 25) (7) = x 3.26  x

25. 2c Trig to solve sides in a  Ex3. Given  A = 47  and c = 12, find a, to the nearest tenth. A B Ca b c 47° 12

26. 1 WP: Trigonometry What do veterinarians usually call little cats with white, black, red and cream colored coats?

27. 1a WP: Trigonometry

28. 1b WP: Trigonometry Ex1. A slide 3.4 m long makes an angle of 35  with the ground. How high is the top of the slide above the ground? 35° ? 3.4m

29. 1c WP: Trigonometry Ex2. A ladder leans against a building forming an angle of 60  with the ground. The base of the ladder is 4 feet from the building. Find the length of the ladder.

30. 1d WP: Trigonometry Ex3. A ladder 14 feet long makes an angle of 53  with the ground as it leans against a barn. How far up the barn does the ladder reach?

31. Unit 8 Review If a 2 +b 2 =c 2 is true, then it is a right triangle. Pythagorean Theorem – Given length of two sides. c P P || = P2P2 For all 45-45-90  s 60° P 2P P3P3 For all 30-60-90 triangles When give a Degree and the length of a side. SCTSCT OAOHHAOAOHHA