Pre-Test. Use trigonometric ratios to find the value of x. Show all your work and round your answer to the nearest tenth.

Transcription

1 Pre-Test Name Date 1. Write the trigonometric ratios for A. Write your answers as simplified fractions. A 6 cm 10 cm sin A cos A C 8 cm B tan A Write the trigonometric ratios for B. Write your answers as simplified fractions. A sin B cm 10 cm cos B C 8 cm B tan B Use trigonometric ratios to find the value of. Show all your work and round your answer to the nearest tenth in mm 39 8 sin 8º 20 20(sin 8º) 1.9 mm cos 39º cos 39 º 15. in ft tan 6º 15 15(tan 6º) 30.8 ft Chapter Assessments 83

2 Pre-Test PAGE 2 6. The cosine of A is approimately Estimate the measure of A. The value of the cosine of an acute angle decreases as the measure of the angle increases. Because cos 5º 0.71 and cos 60º = 0.5, m A should be between 5º and 60º. 7. Josh is using a clinometer to determine the height of a building. He places the clinometer 50 feet from the base of the building and measures the angle of elevation to be 72º. Draw a diagram that models this situation. Then, find the height of the building. Round your answer to the nearest foot. tan 72º 50 50(tan 72 º ) 15 The height of the building is about 15 feet. 72 clinometer 50 ft 8. Louise is using a clinometer to determine the width of a gorge. She stands on one side of the gorge, and uses a clinometer to measure the angle of depression to a point directly across the gorge on the other side. Louise is at an elevation of 358 feet and the point on the other side of the gorge is at an elevation of 2129 feet. She measures a 39º angle of depression. Draw a diagram that models this situation. Then, find the width of the gorge. Round your answer to the nearest foot. tan 51º (tan 51 º ) 161 The width of the gorge is about 161 feet. Louise feet feet 1329 feet 8 Chapter Assessments

3 Post-Test Name Date 1. Write the trigonometric ratios for A. Write your answers as simplified fractions. A 15 mm 39 mm sin A cos A C 36 mm B tan A Write the trigonometric ratios for B. Write your answers as simplified fractions. A 15 mm 39 mm sin B cos B C 36 mm B tan B Use trigonometric ratios to find the value of. Show all your work and round your answer to the nearest tenth in mm sin 26º 8 8(sin 26º) 3.5 mm cos 58º 0 0 cos 58 º 75.5 in. 27 ft tan 71º 27 27(tan 71º) 78. ft Chapter Assessments 85

4 Post-Test PAGE 2 6. The sine of A is approimately Estimate the measure of A. The value of the sine of an acute angle increases as the measure of the angle increases. Because sin 30º = 0.5 and sin 5º 0.71, m A should be between 30º and 5º. 7. Pierre is using a clinometer to determine the height of the Eiffel Tower in Paris. He places the clinometer 80.8 meters from the base of the tower and measures the angle of elevation to be 76º. Draw a diagram that models this situation. Then, find the height of the Eiffel Tower. Round your answer to the nearest meter. tan 76º (tan 76º) 32 The height of the Eiffel Tower is about 32 meters. 76 clinometer 80.8 m 8. Dominique is using a clinometer to determine the horizontal distance between her office and her friend Chantel s office. She stands at her office window, and uses a clinometer to measure the angle of depression to Chantel s office window. Dominique is at an elevation of 80 feet and Chantel s office is at an elevation of 36 feet. She measures a 25º angle of depression. Draw a diagram that models this situation. Then, find the horizontal distance between the offices. Round your answer to the nearest foot. tan 25º tan 25 º Dominique s office feet 36 feet feet 9 The horizontal distance between Chantel s office and Dominque s office is about 9 feet. Chantel s office 86 Chapter Assessments

5 Mid-Chapter Test Name Date Use trigonometric ratios to find the value of. Show all your work and round your answer to the nearest tenth mm 57 5 ft tan 28 º 13 13(tan 28º) 6.9 mm 5 cos 57º 5 cos 57 º 9.2 ft cm 1 8 yd 35 cos 1 º 8 8(cos 1 º ) 6.6 yd tan 35º tan 35 º 38.6 cm Chapter Assessments 87

6 Mid-Chapter Test PAGE 2 5. DeJuan s house is 18 miles due south of Jamie s house. Leslie s house is due east of DeJuan s house and southeast of Jamie s house. Use the following figure to determine how far is Leslie s house from DeJuan s house? Round your answer to the nearest tenth of a mile if necessary. Jamie s house W N E S 18 mi DeJuan s house 65 Leslie s house tan 65º tan 65 º 8. Leslie s house is about 8. miles from DeJuan s house. 6. Michelle s house is 22 miles due north of Jackie s house and northeast of Patrick s house. Patrick s house is due west of Jackie s house. Use the following figure to determine how far is Michelle s house from Patrick s house? Round your answer to the nearest tenth of a mile if necessary. Patrick s house cos 38 º cos 38 º Michelle s house 22 mi Jackie s house Michelle s house is about 27.9 miles from Patrick s house. W N S E 88 Chapter Assessments

7 Mid-Chapter Test PAGE 3 Name Date 7. Your teacher asks you to find the area of a regular octagon. The length of each side of the octagon is 6 millimeters. You know that you need to find the length of the apothem to calculate the area. Use a trigonometric ratio to find the length of the apothem and then find the area of the regular octagon. Round your answer to the nearest tenth if necessary. Hint: The area of a regular polygon can be found ( by using the formula A 1. 2 ) ap a mm 3 Length of apothem: tan 22.5º a 3 a tan 22.5 º a 7.2 mm 1 Area of octagon: A 2 (7.2)(8) 2 A mm The length of the apothem is about 7.2 millimeters and the area of the octagon is about square millimeters. 8. The cosine of A is approimately Estimate the measure of A. The value of the cosine of an acute angle decreases as the measure of the angle increases. Because cos 30º 0.87 and cos 5º 0.71, m A should be between 30º and 5º. Chapter Assessments 89

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9 End of Chapter Test Name Date Use trigonometric ratios to find the value of. Show all your work and round your answer to the nearest tenth in. 27 ft 73 sin 55 º 27 tan 73 º tan 73 º sin 55 º 2. in ft mm sin 8 º 15 15(sin 8 º ) 11.1 mm 61 5 mm cos 61º 5 5(cos 61º) 26.2 mm Chapter Assessments 91

10 End of Chapter Test PAGE 2 5. A ramp at a skateboard park is 30 feet long and has a 30º incline. How high is the top of the ramp? 30 ft 30 sin 30º 30 30(sin 30º) 15 The top of the ramp is 15 feet high. 6. Use a trigonometric ratio to find the width of the following rectangle. Round your answer to the nearest tenth of a centimeter cm cos 59º 37 37(cos 59º) 19.1 The width of the rectangle is about 19.1 centimeters. 7. Paul is making a mosaic design on the floor in a museum. He needs the triangle in the design to cover.25 square feet. Does the triangle he has sketched in his design meet the specifications? 26 2 ft Base of the triangle: tan 26º 2 2 tan 26º.10 Area of the triangle: A 1 2 (.10)(2).10 The area of the triangle is about.10 square feet. So, it will not cover an area of.25 square feet. 92 Chapter Assessments

11 End of Chapter Test PAGE 3 Name Date 8. A regular pentagon is inscribed in a circle with a radius of 10 inches. What is the length of each side of the pentagon? Round your answer to the nearest tenth of an inch. 36 sin 36º 10 10(sin 36º) 5.9 The length of one side of the regular pentagon is about 11.8 inches. 9. Olivia uses a clinometer to measure the height of the observation deck of the Seattle Space Needle. She stands on the observation deck, and uses the clinometer to measure the angle of depression to the top of a building that is 100 feet tall. The building is 66.5 feet from the Space Needle. Olivia measures a 2º angle of depression. Draw a diagram that models this situation. Then, find the height of the observation deck. Round your answer to the nearest foot. Height of the observation deck feet tan 8º tan 8º 20 The height of the observation deck is about 520 feet. 100 ft 66.5 ft 2 8 Chapter Assessments 93

12 End of Chapter Test PAGE 10. Bernard lives in an apartment building in the city, and he can see a skyscraper from his living room window. He would like to know how far his apartment building is from the skyscraper. He uses a clinometer to measure the angle of elevation from his apartment to the top of the skyscraper. The angle of elevation is 38º. He knows that the skyscraper is 630 feet tall and the height of his living room window is 200 feet. Draw a diagram that models this situation. Then, find the distance between Bernard s apartment and the skyscraper. Round your answer to the nearest foot ft 630 ft tan 38º tan 38º 550 The distance from Bernard s living room to the skyscraper is about 550 feet. 9 Chapter Assessments

13 Standardized Test Practice Name Date 1. Eric is flying an airplane at an altitude of 2200 feet. He sees his house on the ground at a 5º angle of depression ft What is Eric s horizontal distance from his house at this point? a. 110 feet b. 220 feet c feet d feet 2. In the following figure, if tan 8, what are sin and cos? a. sin = and cos = b. sin = and cos = c. sin = and cos = d. sin = and cos = Chapter Assessments 95

14 Standardized Test Practice PAGE 2 3. Luis is standing on a street in New York City looking at the top of the Empire State Building with a 30º angle of elevation. He is meters from the Empire State Building m 30 How tall is the Empire State Building? a meters b. 3.2 meters c meters d meters. In the following figure, cos P N P 2 cm M What is the length of PN? a centimeters b. 1. centimeters c. 0 centimeters d. centimeters 96 Chapter Assessments

15 Standardized Test Practice PAGE 3 Name Date 5. In the following diagram, m B 2º and AB 25 feet. Which equation can be used to find the value of? A 25 ft C a. = 25(sin 2º) b. = 25(cos 2º) c. = 25(tan 2º) d. = sin 2º 25 2 B 6. In the following diagram, a 12-foot slide is attached to a swing set. The slide makes a 65º angle with the swing set. Which answer most closely represents the height of the top of the slide? 12 ft 65? sin 65º 0.91 cos 65º 0.2 tan 65º 2.1 a. 5.0 feet b. 5.6 feet c feet d feet Chapter Assessments 97

16 Standardized Test Practice PAGE 7. Which of the following statements is true? a. As the measure of the angle increases, the value of the sine and the cosine increases. b. As the measure of the angle increases, the value of the sine and the cosine decreases. c. As the measure of the angle increases, the value of the sine and the tangent increases. d. As the measure of the angle increases, the value of the cosine and the tangent decreases. 8. A regular heagon is inscribed in a circle with a radius of 10 meters. What is the length of each side of the heagon? 10 m a. 5 meters b. 5 3 meters c. 10 meters d. Cannot be determined 98 Chapter Assessments

17 Standardized Test Practice PAGE 5 Name Date 9. The cos A Which of the following statements must be true? a. The measure of A is between 30º and 5º. b. The measure of A is between 5º and 60º. c. The measure of A is between 60º and 75º. d. The measure of A is between 75º and 90º. 10. Which of the following statements is NOT true? a. The cosine of an acute angle is always less than or equal to one. b. The sine of an acute angle is always less than or equal to one. c. The tangent of an acute angle is always less than or equal to one. d. The value of the sine of an angle divided by the value of the cosine of the angle is equal to the value of the tangent of the angle. Chapter Assessments 99

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