1. Warmup 1. Draw and label a right triangle.
2-4 Label legs and hypotenuse

2. Applying Right Triangles and Trigonometry
Chapter 8 p. 394

3. How to apply right triangles and trigonometry to solve problems?
Use the Pythagorean Theorem and its converse,
Use the properties of 45-45º-90º and º-60º-90º triangles,
Use trigonometry to solve triangles, and
Choose the appropriate strategy for solving a problem.

4. Pythagorean Theorem: a2 + b2 = c2

5. Pythagorean Theorem: a2 + b2 = c2 and its converse
Given a and b:
Given (a or b) and c
20 ft

6. Pythagorean Triples
A right triangle where the sides are in the ratio of integers. (Integers are whole numbers like 3, 12 etc) For example, the following are Pythagorean triples:
There are infinitely many pythagorean triples. Here are the first few: 3:4:5 , 6:8:10 , 5:12:13, 9:12:15 , 8:15:17 etc...

7. Twitter #pytthm If AC=25 and BC=15, find DC. A B E D C a2 + b2 = c2
625 – 225 = 400
Sqrt 400 = 20

8. Warm-up: Pythagorean Theorem: a2 + b2 = c2
1. Find the missing side length. A. B.
2. Tell if the measures can be the side lengths of a triangle. If so, determine if it is a right triangle.
A. 9, 40, 41
B. 8, 13, 23 X 3m 9m X
7ft
11ft

9. Special Right Triangles
45-45º-90º
30º-60º-90º
Hypotenuse is opposite of 90 degree angle
Hypotenuse is opposite of 90 degree angle
Short leg is opposite of 30 degree angle
Legs are congruent
Long leg is opposite of 60 degree angle
Terms: Leg, Hypotenuse, Short Leg, Long Leg

10. Special Right Triangles
30 –
L = hyp √2
Hyp = L√2
Hyp = 2(SL)
SL = hyp or SL = LL √3
LL = SL√3
2. If <A=60º & AC=14, find x and y. A x B y C
1. If <A=45º & BC=4, find x and y. x
A B y C
x = short leg = 14/2 = 7
y =long leg = 7√3
x = leg = 4
y = hypotenuse =
4√2

11. Practice: Quiz next class Pythagorean Theorem: a2 + b2 = c2
Special Triangles, find x.
30 –
L = hyp √2
Hyp = L(√2)
Hyp = 2(SL)
SL = hyp or SL = LL √3
LL = SL(√3)

12. Warm-Up 2. If <A =60º & AB =5, solve the triangle.
B C
3. If <A= 45º & AC=5√6, solve the triangle.
1. Use Pythagorean Thm.
30 m
25 m x

13. √ Practice: Pythagorean Theorem: a2 + b2 = c2
Special Triangles, find x.
30 –
L = hyp √2
Hyp = √2(L)
Hyp = 2(SL)
SL = hyp or SL = LL √3
LL = √3(SL)

14. Indiv. Practice 2. If <A =60º & AC=18, find AB and BC. A
1. If AC=26 and AD=10, find BC, DB, AB and DC. A B E D C

15. Quiz: Pythagorean Theorem and Special Right Triangles
1. If AB=5 & BC=9, find AC.
A C B
2. Find AC, if AB=30 & BC=16. A
B C
Special Right triangles
3. If <A=60º & AC=14, find x and y. A x
B y C
4. If <A=45º & BC=4, find x and y x
A B y C

16. √ Quiz: Pythagorean Theorem and Special Right Triangles
1. If AB=5 & BC=9, find AC.
A C B
2. Find AC, if AB=30 & BC=16. A
B C
Special Right triangles
3. If <A=60º & AC=14, find x and y. A x
B y C
4. If <A=45º & BC=4, find x and y x
A B y C

17. Trigonometry Ratios in Right Triangles
To find trigonometric ratios using right triangles
To solve problems using trigonometric ratios

18. Trigonometry What is Trigonometry?
The study of trigonometry involves triangle measurement.
A ratio of the lengths of the sides of a right triangle is called a trigonometric ratio.

19. Terms used in Trigonometry
Used in acronym SOHCAHTOA

20. Trigonometric Ratios SOH CAH TOA
Abbreviation
Definition
Sine <A
sin A
Leg opp <A = a
Hypotenuse c
Cosine <A
cos A
Leg adj <A = b
Tangent <A
Tan A
Leg adj <A b

21. Practice
Worksheet
Video

22. Warm-Up
1.Define SOHCAHTOA. 2.
3. y m
x ft
y ft
73º
24 ft

23. Practice
√ Worksheet

24. Quiz time: trigonometric ratios
Complete study guides

25. SOHCAH TOA ` Pythagorean Theorem a2 + b2 = c2 CHP 8 TEST
Right Triangles
CHP 8
TEST
30 –
L = hyp √2
Hyp = L(√2)
Hyp = 2(SL)
SL = hyp or SL = LL √3
LL = (SL)√3
SOHCAH TOA