Warmup 1 Draw and label a right triangle

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

Applying Right Triangles and Trigonometry Chapter 8 p. 394

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 30º -60º-90º triangles, Use trigonometry to solve triangles, and Choose the appropriate strategy for solving a problem.

Pythagorean Theorem: a 2 + b 2 = c 2

Pythagorean Theorem: a 2 + b 2 = c 2 and its converse Given a and b: 20 ft Given (a or b) and c

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. . .

Twitter #pytthm If AC=25 and BC=15, find DC. A B E D C a 2 + b 2 = c 2 152 + b 2 = 252 625 – 225 = 400 Sqrt 400 = 20

Warm-up: Pythagorean Theorem: a 2 + b 2 = c 2 1. Find the missing side length. A. 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 3 m 9 m B. X 7 ft 11 ft 2. Tell if the measures

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

Special Right Triangles 45 - 90 L = hyp √ 2 30 – 60 -90 Hyp = 2(SL) SL = hyp 2 Hyp = L√ 2 LL = SL√ 3 1. If <A=45º & BC=4, find x and y. x = leg = 4 y = hypotenuse = 4√ 2 A x y or SL = LL √ 3 B C 2. If <A=60º & AC=14, find x and y. x = short leg = 14/2 A =7 y =long leg = 7√ 3 x B y C

Quiz next class Practice: Pythagorean Theorem: a 2 + b 2 = c 2 Special Triangles, find x. 45 - 90 L = hyp √ 2 Hyp = L(√ 2) 30 – 60 -90 Hyp = 2(SL) SL = hyp 2 LL = SL(√ 3) or SL = LL √ 3

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

√ Practice: Pythagorean Theorem: a 2 + b 2 = c 2 Special Triangles, find x. 45 - 90 L = hyp √ 2 Hyp = √ 2(L) 30 – 60 -90 Hyp = 2(SL) SL = hyp 2 LL = √ 3(SL) or SL = LL √ 3

Indiv. Practice 1. If AC=26 and AD=10, find BC, DB, AB and DC. 2. If <A =60º & AC=18, find AB and BC. A B B 3. If <A= 45º & AC= 3, find AB and BC. A C B A C E D C

Quiz: Pythagorean Theorem and Special Right Triangles Pythagorean Theorem 1. If AB=5 & BC=9, find AC. A C B 2. Find AC, if AB=30 & BC=16. A 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 B C C

√ Quiz: Pythagorean Theorem and Special Right Triangles Pythagorean Theorem 1. If AB=5 & BC=9, find AC. A C B 2. Find AC, if AB=30 & BC=16. A 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 B C C

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

What is Trigonometry? 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.

Terms used in Trigonometry Used in acronym SOHCAHTOA

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

Practice Worksheet Video

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

Practice √ Worksheet

Quiz time: trigonometric ratios Complete study guides

Pythagorean Theorem ` a 2 + b 2 = c 2 C H P 8 T E S T 45 - 90 L = hyp √ 2 Hyp = L(√ 2) Right Triangles 30 – 60 -90 Hyp = 2(SL) SL = hyp 2 or SL = LL √ 3 LL = (SL)√ 3 SOHCAH TOA