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4-69. Marta arrives for her math test only to find that she has forgotten her calculator. She decides to complete as much of each problem as possible. a. In the first problem on the test, Marta has to solve for the length x in the triangle shown at right. Using her algebra skills, she writes and solves an equation. Her work is shown below. Explain what she did in each step. 29 sin 25° = 𝑥 x(sin 25°) = 29 29 x= sin 25 b. <- Write down! Marta’s answer in part (a) is called an exact answer. Now use your calculator to help Marta determine the approximate value of x. 68.62 c. Marta’s teammate, Ziv, said he solved it differently but still got the 29 same answer. He started with the equation cos 65°= . Explain 𝑥 why this equation must give the same answer. Because 65 and 25 are complementary angles, but the 29 becomes the adjacent with 65 degrees. 4-69. d. Solve for y in the diagram at right in two ways, using both sine and cosine ratios. Make sure both strategies result in the same answer. 𝑦 5 sin 53° = 5(sin 53°) = y y = 3.99 𝑦 cos 37° = 5 5(cos 37°) = y y = 3.99 4.2.2 SELECTING A TRIG TOOL November 30, 2015 Objectives • CO: SWBAT solve for missing sides using sine, cosine, or tangent. • LO: SWBAT verbally develop strategies in their teams to recognize which trigonometric ratio to use based on the relative position of the reference angle and the given sides involved. Progress Chart a-c Purple Stripes Blue Green Pink Orange Yellow Red d-f g-i Team Roles • Resource Manager: Pull ideas from the team. Ask questions such as, “Does anyone have an idea?” and “Which side is opposite the angle?”. • Task Manager: Listen for statements and reasons. Ask questions such as, “Why did you choose that ratio?” and “How did you know that side is opposite?”. • Facilitator: Keep the team together and keep the discussion going. Ask questions such as, “Did everyone agree with her statement?” and “Is everyone ready to move on to the next question?”. • Recorder/Reporter: Create large sketches of diagrams that can be seen clearly by all team members. Ask questions such as, “What strategies can we share with the class?”. “Choosing a Trig Tool” a. b. c. d. e. f. g. h. i. Sine -> x ≈ 8.92 x = 8 (slope ratio is 1) Cosine x ≈ 37.13 Sine -> x ≈ 14.20 x = 16 using similarity ratio from problem 4-57 Sine -> x = 21 x = 0 (angle collapses) Cosine -> x ≈ 0.88 Tangent -> x ≈ 10.80 4-70. In problem 4-68, you used trigonometric tools to solve for a side length. But do you have a way to determine an angle measure? Examine the triangles below. Do any of them look familiar? How can you use information about the side lengths to help you figure out the reference angle (θ)? Your Trig Table Graphic Organizer from Chapter 3 may be useful. 9 tan𝜃= 9 𝜃 = 45° 1 tan𝜃= 5 𝜃 = 11° 1 cos𝜃= 2 𝜃 = 60°