Right Triangle Trigonometry Essentials

Delve into the fundamentals of right triangle trigonometry, exploring the relationships between angles and sides. Understand the concept of labeling the sides, determining trigonometric ratios, finding values using calculators, and applying trigonometric ratios to solve for sides and angles. Enhance your knowledge of SOH-CAH-TOA and its role in trigonometry.

• Trigonometry
• Triangles
• Ratios
• Calculations
• SOH-CAH-TOA

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Uploaded on Feb 16, 2025 | 0 Views

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1. Right Triangle Trigonometry ~ TRIGONOMETRY IS THE STUDY OF TRIANGLES AND THEIR MEASURES.

2. Labeling the sides What side is OPPOSITE of Angle A? What side is ADJACENT to Angle A? What side is OPPOSITE of Angle B? What side is ADJACENT to Angle B?

3. Labeling the sides What side the HYPOTENUSE of the triangle? What side is OPPOSITE of Angle A? What side is ADJACENT to Angle A? What side is OPPOSITE of Angle B? What side is ADJACENT to Angle B?

4. Finding the Trigonometric Ratios Each angle measure has a trigonometric value that is equivalent to a ratio between the sides. SOH-CAH-TOA sin? =?? ? cos? =? ? tan? =??? ?? ?? ? ?

5. Finding the Trigonometric Ratios Each angle measure has a trigonometric value that is equivalent to a ratio between the sides. SOH-CAH-TOA sin? =?? ? cos? =? ? tan? =??? ?? ?? ? ?

6. Finding the Trigonometric Value ~ Grab your calculator or open a scientific calculator on your browser. https://www.desmos.com/scientific To get to the next step in the process you must know how to calculate sine, cosine, and tangent in your calculator. sin 23 DESMOS cos 45 tan 87

7. Using Trigonometric Ratios to find a side SOH-CAH-TOA Let s find side b. 1. Locate the angle you are given 2. Determine the ratio you are going to use. 3. Set up the ratio 4. MATH! (use your calculator) sin? =?? ? ?? cos? =? ? ?? tan? =??? ? ?

8. Using Trigonometric Ratios to find a side SOH-CAH-TOA Let s find side c. 1. Locate your angle 2. Determine the ratio you are going to use. 3. Set up the ratio 4. MATH! (use your calculator) sin? =?? ? ?? cos? =? ? ?? tan? =??? ? ?

9. Using Trigonometric Ratios to FIND AN ANGLE SOH-CAH-TOA sin? =?? ? ?? Every mathematical operation has an INVERSE Addition ~ Subtraction Multiplication ~ Division Square ~ Square Root cos? =? ? ?? And trig functions have trig INVERSE functions sin?~sin 1? tan? =??? ? ? ????~cos 1? tan?~tan 1?

10. Finding INVERSE Trig Values ~ Grab your calculator again. https://www.desmos.com/scientific Find the missing angle sin? = 0.29 cos? = 0.18 tan? = 1.23

11. Finding INVERSE Trig Values to find ANGLES Find the missing angle 9 12 cos? =

12. Finding INVERSE Trig Values to find ANGLES Find the missing angle sin? =?? ? ?? 1. Locate the angle you are trying to determine 2. Decide the ratio you will need to use. 3. Set up the trig ratio cos? =? ? ?? tan? =??? ? ? 4. Use the *inverse* function to find the angle.

13. PLEASE COMPLETE the following worksheet: Right Triangle Trig Objective #2 This worksheet can also be found in your printed packet.

14. Quizzes and Extra Resources: Trigonometry Quiz #1 Trigonometry Quiz #2 Khan Academy Right Triangle Trigonometry