Teacher Outline: 6.1 Right Triangle Trigonometry

I. Suggested Pacinga. 2 day Traditionalb. 1 day Block

II. Warm Up Problemsa. Given the right triangle below, find the missing side.19.01

b. Given the triangle below, find the missing angle.

41 °

c. Using the triangle below find the missing sides and angle.

28 ° ,19.62

III. Learning Objectivesa. Suggested Content Objective: The student will be able to convert back and forth

between degree and degree minutes seconds, evaluate trigonometric ratios from any angle in a right triangle by hand and by use of a graphing calculator.

b. Suggested Approach: Students will get a basic understanding of the content objectives using think-pair-share, and teacher led instruction.

IV. Topic Outlinea. Converting Between Degrees and DMS (Degree Minutes Seconds)

i. Examples include:1. Write 35 °15 ' 25 in decimal form35.2575 °

2. Write 31 °24 ' 45 in decimal form31.4125 °

3. Write 48.3625 ° in DMS form48 ° 21' 45

4. Write 42.5025 ° in DMS form42 ° 30 ' 9

b. Evaluating Six Trigonometric Ratiosi. Examples include:

1. Given the Triangle below find the six trigonometric ratios for Ɵ.

6.1 Right Triangle Trigonometry Page 1Week 3.1

Teacher Outline: 6.1 Right Triangle Trigonometry

sin θ= 513

cosθ=1213

tanθ= 512

csc θ=135

secθ=1312

cot θ=125

2. Given the Triangle below find the six trigonometric ratios for Ɵ.

sin θ=1.63.4

cosθ= 33.4

tanθ=1.63

csc θ=3.41.6

secθ=3.43

cot θ= 31.6

c. Evaluating Six Trigonometric Ratios on a Calculatori. Examples include:

1. Evaluate all six trigonometric ratios of 20 °.

sin 20 °=0.3420 cos20 °=0.9397 tan20 °=0.3640

csc 20 °=2.9235 sec20 °=1.0642 cot 20 °=2.7475

2. Evaluate all six trigonometric ratios of 15 °.

sin 15 °=0.2588 cos15 °=0.9659 tan15 °=0.2679

csc 15 °=3.8637 sec15 °=1.0353 cot 15 °=3.7321

6.1 Right Triangle Trigonometry Page 2Week 3.1

Teacher Outline: 6.1 Right Triangle Trigonometry

d. Evaluating Trigonometric Ratios of Special Anglesi. Examples include:

1. Evaluate all 6 trig ratios for 30 ° ,60 ° , and 45 °.

e. Application Problemsi. Angles of Elevation and Depression

ii. Examples Include:1. Sighting the top of a building a surveyor measured the angle of

elevation to be 22o. The transit is 5 feet above the ground and 300 feet from the building. Find the building’s height.

a≈121h≈5+121≈126

2. A building that is 21 meters tall casts a shadow 25 meters long. Find the angle of elevation of the sun to the nearest degree.

6.1 Right Triangle Trigonometry Page 3Week 3.1

Teacher Outline: 6.1 Right Triangle Trigonometry

tan−1θ=2125;θ≈40 °

6.1 Right Triangle Trigonometry Page 4Week 3.1