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Date: 4.3(a) Notes: Trig. Ratios Lesson Objective: Use right triangles to evaluate trig functions. CCSS: F-TF Extend the domain of trigonometric functions using the unit circle. You will need: calculator Lesson 1: Trig. Definitions Trigonometric (trig) Ratio: A ratio of 2 sides of a right triangle. Reference Angle: The acute angle we are referring to or are using. Opposite Leg: The leg across from the / that is not the hypotenuse. Adjacent Leg: The leg next to the / that is not the hypotenuse. Hypotenuse: The side opposite the right / . Lesson 1: Trig. Definitions BC is _________________ / A. AB is ________________ / A. AC is the ___________________. A B C Lesson 2: SOH-CAH-TOA Game Draw the figure. Choose the correct answer. Write each question and answer in your notes. Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game A. Opposite / X Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game B. Adjacent to / X Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game C. Hypotenuse Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game D. Adjacent to Leg 1 Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game E. Opposite / Y Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game F. Opposite Leg 1 Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game G. Opposite / Z Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game H. Adjacent to Leg 3 Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game I. Adjacent to / Z Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game J. Opposite / Y Z 1 Y 2 3 X Lesson 2: SOH-CAH-TOA Game K. Opposite Leg 3 Z 1 Y 2 3 X Lesson 3: Trig. Ratios “SOH” Lesson 3: Trig. Ratios “CAH” Lesson 3: Trig. Ratios “TOA” Lesson 3: Trig. Ratios “SOH-CAH-TOA” COSECANT = 1 = Hypotenuse csc SIN Opposite SECANT = 1 = Hypotenuse sec COS Adjacent COTANGENT = 1 = Adjacent cot TAN Opposite Lesson 3: Trig. Ratios Find the values of the 6 trig. functions of θ. Lesson 4: Angle of Elevation and Depression Lesson 4: Angle of Elevation and Depression A. Suppose the car is 150 feet from the building and the observer’s angle of depression is 40°. What is the distance of the line of sight below the observer? Lesson 4: Angle of Elevation and Depression B Sighting the top of a building, a surveyor measured the angle of elevation to be 22°. The transit through which the surveyor sights the building’s angle of elevation is 5 feet above the ground and 300 feet from the building. Draw a diagram, then find the building’s height. 4.3(a): Do I Get It? Yes or No 1. Find the values of the 6 trig. functions of the other acute angle, β,. 4.3(a): Do I Get It? Continued 2. A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as 78.3°. How Tall is the Washington Monument? 4.3(a): Do I Get It? Continued 3. Find the length c of the skateboard ramp.