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Student: Class: Date: Trigonometry in general triangles Student Activity Sheet 2; use with Exploring “Law of Sines” 1. In commercials, the Straight Shot Screamer is advertised as “120 feet of pure excitement!” Use what you know about right triangle trigonometry to determine the unknown side lengths and angle measure. 77.786 59.588 65.270 24.624 2. Using the completed triangle from question 1, write two different sine ratios that involve the length 50 ft. Isolate the 50 in each equation and write a relationship between the two sine values and sides of the triangle. Copyright 2013 Agile Mind, Inc. ® Content copyright 2013 Charles A. Dana Center, The University of Texas at Austin Page 1 of 1 With space for student work Student: Class: Date: Trigonometry in general triangles Student Activity Sheet 2; use with Exploring “Law of Sines” 3. Fill in the blanks to develop the proof of the sine-to-side relationship. c sinA = a sinC h h sinA = 1 ; sinC = 1 c a Copyright 2013 Agile Mind, Inc. ® Content copyright 2013 Charles A. Dana Center, The University of Texas at Austin c sinA = h1; a sinC = h1 sinA sinC = a c Page 2 of 2 With space for student work Student: Class: Date: Trigonometry in general triangles Student Activity Sheet 2; use with Exploring “Law of Sines” 4. Fill in the table with the trig ratios for some special angles and their supplements. For each angle, think about what the sides of the reference triangle would be and calculate each trig ratio. a° sin a° cos a° tan a° 30° 45° 60° 120° 135° 150° 5. Fill in the blanks to summarize your findings about the sine value of supplementary angles. supplementary 180° 90° complementary are always equal always add up to 1 The degree measures of two angles add up to . The degree measures of two angles add up to . The sine values of two Copyright 2013 Agile Mind, Inc. ® Content copyright 2013 Charles A. Dana Center, The University of Texas at Austin angles Page 3 of 3 With space for student work . Student: Class: Date: Trigonometry in general triangles Student Activity Sheet 2; use with Exploring “Law of Sines” 6. In the triangle above, what is the relationship between ∠ABC and ∠ABD? What does this tell you about the sine value of the two angles? 7. Use ∆ABD to help you write a ratio for sin ∠ABC. 8. You have two sine ratios involving h2: sin B = and sin C = . Use the two ratios to write the sine-to-side relationship from earlier. Start by isolating h2 in each ratio. Copyright 2013 Agile Mind, Inc. ® Content copyright 2013 Charles A. Dana Center, The University of Texas at Austin Page 4 of 4 With space for student work Student: Class: Date: Trigonometry in general triangles Student Activity Sheet 2; use with Exploring “Law of Sines” 9. Write the Law of Sines. 10. Use the Law of Sines to find the base of the Straight Shot Screams, from the foot of the steps to the end of the slide. (Hint: use the 40° ratio since it does not contain any approximate values.) Copyright 2013 Agile Mind, Inc. ® Content copyright 2013 Charles A. Dana Center, The University of Texas at Austin Page 5 of 5 With space for student work Student: Class: Date: Trigonometry in general triangles Student Activity Sheet 2; use with Exploring “Law of Sines” 11. R EINFORCE Use the Law of Sines to solve for the missing side lengths or angle measures in the examples below. a. x= y= z= x= y= z= b. Copyright 2013 Agile Mind, Inc. ® Content copyright 2013 Charles A. Dana Center, The University of Texas at Austin Page 6 of 6 With space for student work Student: Class: Date: Trigonometry in general triangles Student Activity Sheet 2; use with Exploring “Law of Sines” 12. Sketch the different kinds of triangles formed by the Dunkin’ Swing ride. 13. When two sides and one nonincluded angle are given, describe the types of triangles that might result. 14. In each of the triangles below, you are given two side lengths and the measure of the nonincluded angle. Solve each of the triangles for the missing angle measure. Explain your solutions. a. Copyright 2013 Agile Mind, Inc. ® Content copyright 2013 Charles A. Dana Center, The University of Texas at Austin Page 7 of 7 With space for student work Student: Class: Trigonometry in general triangles Student Activity Sheet 2; use with Exploring “Law of Sines” b. c. Copyright 2013 Agile Mind, Inc. ® Content copyright 2013 Charles A. Dana Center, The University of Texas at Austin Page 8 of 8 With space for student work Date: Student: Class: Date: Trigonometry in general triangles Student Activity Sheet 2; use with Exploring “Law of Sines” 15. R EINFORCE a. In ΔABC, m∠A = 36º, a = 7, and b = 10. Determine whether ∠B exists. If so, find all possible measures of ∠B. b. Sketch all possible triangles with these measures. 16. R EINFORCE From fire towers Q and R, located 18 miles apart, a fire is sighted at point F. If m∠FRQ = 70º and m∠FQR = 48º, find the distance (to the nearest mile) from point F to the closest fire tower. Sketch a diagram as part of your solution. Copyright 2013 Agile Mind, Inc. ® Content copyright 2013 Charles A. Dana Center, The University of Texas at Austin Page 9 of 9 With space for student work