# Unit 3: Right Triangle Trigonometry

UNIT 3: RIGHT TRIANGLE TRIGONOMETRY Vocabulary Builder Daily Agenda Similar Triangles Square Root leg Pythagorea n Theorem Simplest radical form 45-45-90 Triangle Hypotenus e Variable 30-60-90 Daily Agenda

Daily Agenda UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.1 Trigonometric Ratios Daily 3.1 Agenda Trigonometric Ratio square root perfect square radical expression radicand perfect square Daily 3.1 Agenda Trigonometric Ratio

5 30 8 18 14 23 Check for Understanding 2 10 3 3 Daily 3.1 Agenda Trigonometric Ratio

right triangle equals hypotenuse side lengths Daily 3.1 Trigonometric Agenda Example 2/ Check for Understanding 13) 14) 2 2 4 +8 = 2 1 6+64= 2 8 0= 2

4 5= Ratio 15) 2 2 2 +3.9 2=11 2 2 2 +15.21=121 2 6 +3 = 3 6+ 9= 4 5= 2 3 5=

2 =105.79 =10.29 Daily 3.1 Trigonometric Ratio Agenda We can use the Pythagorean Theorem to determine if 3 given numbers represent the sides of a right triangle. Example 3: A. 5, 5, 10 += 25 + 25 = 100 50 100 NO C. 6, 8, 10 B. 9, 12, 15 += 81 + 144 = 225 225 = 225 YES D. 4, 6,

Daily 3.1 Trigonometric Ratio Agenda Dividing into 2 Similar SubTriangles Daily 3.1 Trigonometric Ratio Agenda Dividing into 2 Similar SubTriangles 15:39 :36 :15 36:39 :36 :15 15:36 : : Daily 3.1 Trigonometric Ratio Agenda Dividing into 2 Similar SubTriangles 3. Use the values of the ratios you calculated to find the length of and

Daily 3.1 Agenda Trigonometric Ratio hypotenuse adjacent opposite Daily 3.1 Trigonometric Agenda Example 4 Ratio Daily 3.1 Trigonometric Agenda Check for Understanding

Ratio Daily 3.1 Trigonometric trigonometric ratio Agenda SOH CAH TOA right length acute Ratio Daily Agenda Daily 3.1 Trigonometric Ratio Agenda Example 5 SOH CAH TOA 20 4

15 3 16 8 30 15 14 7 24 48 15 3 25 5 30 15 34 17 48 24

50 25 5 Question Wrap-Up 1. The Pythagorean Theorem helps you solve for a missing ________ of a triangle. 2. We apply the Pythagorean Theorem to _______ triangles. 3. Simplify 4. Write the acronym used to trigonometric functions. 5. The only trig function that doesnt use the hypotenuse is the ________ function. UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.2 Finding Sides and Angles of Right Triangles Daily 3.2 Missing Sides and Ang function Agenda angle output

s input Daily 3.2 Missing Sides and Ang Agenda x x sin = sin 19 = 11 11 sin 19 = 3.58 = x

cos = sin = 19.2 11 cos 46 = sin 34 = 19.2 11 = = cos 46 sin 34 =27.64 =19.67 Daily 3.2 Missing Sides and Ang Check for Understanding Agenda

x tan26 = 14.63 = tan50 = =15.49 tan20 = =6.92 Daily 3.2 Missing Sides and Ang Agenda sin cos tan

-1 -1 -1 Example 2 = 5 5 = 1 tan 1 (1 )= = tan 1 5 12 5 =

12 ( ) 45 = 22.6 = = cos 1 40 42 40 = 42 ( ) 17.8 = Daily 3.2 Missing Sides and Ang Example 3 Agenda cos

1 15 = 28 ( ) 57.6 = sin 1 19 = 23 ( ) 55.7 = cos 1 70 = 86

( ) 35.5 = 5 Question Wrap-Up 1. The side across from the discussed angle is called/labeled __________. 2. Simplify Show full break-down work. 3. Inverse trig functions help solve for missing ________. 4. Solve for x. UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.3 Sine and Cosine of Complementary Angles 3.3 Sine and Cosine of Complementary An Daily What am I learning Agenda today? 180

90 x G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? 90 complementar y Find the complement of sine and cosine How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door

opposite angle cosin e x 3.3 Sine and Cosine of Complementary An Daily What am I learning Agenda today? G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? Find the complement of sine and cosine

Check for Understanding How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door

3.3 Sine and Cosine of Complementary An Daily Example 2 What am I learning Agenda today? G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? Find the complement of sine and cosine How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door

3.3 Sine and Cosine of Complementary An Daily Example 2 continued What am I learning Agenda today? G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do

today? Then mQ = 60 Find the complement of sine and cosine How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door . . . . Sin A and Cos B are the same which means the complement of sine and cosi equal. 3.3 Sine and Cosine of Complementary An Daily

Example 3 What am I learning Agenda today? G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? . Find the complement of sine and cosine How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door .

3.3 Sine and Cosine of Complementary An Daily What am I learning Example 4 Agenda today? G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? Find the complement of sine and cosine How will I show you that Ive learned it?

5 Question Daily Assessment Daily Ticket out the Door A 13 52 +122 = 2 5 2 5+144= 2 13 1 69= 2 13= C

12 B A 37 122 +35 2= 2 2 1 44 +1225= 1 369= 2 37= 35 H 37 12 T 3.3 Sine and Cosine of Complementary An Daily

What am I learning Check for Understanding Agenda today? G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? Find the complement of sine and cosine How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door 10

8 2+ 62 = 2 6 4+ 36= 2 1 00= 2 10= T.O.T.D. Slide UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.4 Application of Trig 3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda

today? G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? Use the Pythagorean Theorem to Solve Right Triangles Use Trigonometric Ratios to Solve Right Triangles How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door

solve side lengths angle The length of two sides The length of 1 side and 1 acute angle The length of 1 side and 1 trigonometric ratio 3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda today? G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied

problems What am I going to do today? Use the Pythagorean Theorem to Solve Right Triangles Use Trigonometric Ratios to Solve Right Triangles How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door 9.4 2 9. 4 19 71

3.12 +8.9 2= 2 9 .61+79.21= 2 8 8.82= 2 9.42= tan 1 3.1 = 8.9 ( ) 19.2 = R = 90 19.2 = 70.8 3.4 Solve Right Triangles using Daily Trigonometric Ratios

What am I learning Agenda today? G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? Use the Pythagorean Theorem to Solve Right Triangles Use Trigonometric Ratios to Solve Right Triangles How will I show you that Ive learned it? 5 Question Daily Assessment

Daily Ticket out the Door Example 2 sin 32 = 3.9 2 6.27 3.9 2 6.27 58 7.4 3.92= 2 +3.9 2=7.4 2 2 +15.21=54.76 2 =39.55 =6.27

C = 90 32 = 58 3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda today? G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? Use the Pythagorean

Theorem to Solve Right Triangles Use Trigonometric Ratios to Solve Right Triangles How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door angle of elevation angle of depression 3.4 Solve Right Triangles using Daily Trigonometric Ratios

What am I learning Agenda today? G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? Use the Pythagorean Theorem to Solve Right Triangles Use Trigonometric Ratios to Solve Right Triangles How will I show you that Ive learned it? 5 Question Daily Assessment

Daily Ticket out the Door Example 3 3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda today? G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do

today? Use the Pythagorean Theorem to Solve Right Triangles Use Trigonometric Ratios to Solve Right Triangles How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door Check for Understanding 3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning

Agenda today? G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? Example 4 Use the Pythagorean Theorem to Solve Right Triangles Use Trigonometric Ratios to Solve Right Triangles How will I show you that Ive learned it?

5 Question Daily Assessment Daily Ticket out the Door 618.75 ft 3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda today? G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied

problems What am I going to do today? Example 5 Use the Pythagorean Theorem to Solve Right Triangles Use Trigonometric Ratios to Solve Right Triangles How will I show you that Ive learned it? 5 Question Daily Assessment Daily Ticket out the Door 991.86 ft

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