Unit 2 Review Short nswer 1. Find the value of x. Express your answer in simplest radical form. 30º x 3 24 y 6 60º x 2. The size of a TV screen is given by the length of its diagonal. The screen aspect ratio is the ratio of its width to its height. The screen aspect ratio of a standard TV screen is 4:3. What are the width and height of a 27" TV screen? 5. Write the trigonometric ratio for cos X as a fraction and as a decimal rounded to the nearest hundredth. Y height 27" 15 9 X 12 Z width 3. Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. 25 20 6. Use your calculator to find the trigonometric ratios sin 79, cos 47, and tan 77. Round to the nearest hundredth. 7. Use your calculator to find the trigonometric ratios sin 49, cos 50, and tan 45. Round to the nearest hundredth. 8. Find GH. Round to the nearest hundredth. G 4. Find the values of x and y. Express your answers in simplest radical form. F 35 18.4 in. H
9. Jessie is building a ramp for loading motorcycles onto a trailer. The trailer is 2.8 feet off of the ground. To avoid making it too difficult to push a motorcycle up the ramp, Jessie decides to make the angle between the ramp and the ground 15. To the nearest hundredth of a foot, find the length of the ramp. 10. Find the sine and cosine of the acute angles in the right triangle. 1.3 cm 2 3 1.2 cm 1 0.5 cm 15. Use your calculator to find the angle measures to the nearest tenth of a degree. 16. Find to the nearest hundredth. 53 45 4 C 2 28 17. Classify each angle in the diagram as an angle of elevation or an angle of depression. 11. Find the sine and cosine of the acute angles in the right triangle. 1 3 4 2 169 119 18. The largest Egyptian pyramid is 146.5 m high. When Rowena stands far away from the pyramid, her line of sight to the top of the pyramid forms an angle of elevation of 20 with the ground. What is the horizontal distance between the center of the pyramid and Rowena? Round to the nearest meter. 120 19. n eagle 300 feet in the air spots its prey on the ground. The angle of depression to its prey is 15. What is the horizontal distance between the eagle and its prey? Round to the nearest foot. 12. Write cos 16 in terms of the sine. 13. Write sin 74 in terms of the cosine. 14. Use the trigonometric ratio to determine which angle of the triangle is. 20. pilot flying at an altitude of 1.8 km sights the runway directly in front of her. The angle of depression to the beginning of the runway is 31. The angle of depression to the end of the runway is 23. What is the length of the runway? Round to the nearest tenth of a kilometer.
Unit 2 Review nswer Section SHORT NSWER 1. NS: x = Pythagorean Theorem Substitute 3 for a, 6 for b, and x for c. Simplify. Find the positive square root. Simplify the radical. PTS: 1 DIF: 2 REF: 1af8a14a-4683-11df-9c7d-001185f0d2ea OJ: 9-1.1 Using the Pythagorean Theorem ST: MCC9-12.G.SRT.8 LOC: MTH.C.10.05.10.05.01.001 MTH.C.11.03.02.05.02.002 TOP: 9-1 The Pythagorean Theorem KEY: Pythagorean Theorem side length DOK: DOK 1 2. NS: width: 21.6 in., height: 16.2 in. Let 3x be the height in inches. Then 4x is the width of the TV screen. Pythagorean Theorem Substitute 4x for a, 3x for b, and 27 for c. Multiply and combine like terms. Divide both sides by 25. in. Find the positive square root. Width: Height: in. in. PTS: 1 DIF: 2 REF: 1afadc96-4683-11df-9c7d-001185f0d2ea OJ: 9-1.2 pplication NT: NT.CCSS.MTH.10.9-12.G.SRT.8 ST: MCC9-12.G.SRT.8 LOC: MTH.C.10.05.10.05.01.001 MTH.C.11.03.02.05.02.002 TOP: 9-1 The Pythagorean Theorem KEY: Pythagorean Theorem side length DOK: DOK 1 3. NS: The missing side length is 15. The side lengths form a Pythagorean triple because they are nonzero whole numbers that satisfy the equation. Pythagorean Theorem Substitute 20 for a and 25 for c. Multiply and subtract 400 from both sides. Find the positive square root.
The side lengths are nonzero whole numbers that satisfy the equation triple., so they form a Pythagorean PTS: 1 DIF: 1 REF: 1afd3ef2-4683-11df-9c7d-001185f0d2ea OJ: 9-1.3 Identifying Pythagorean Triples ST: MCC9-12..REI.4b LOC: MTH.C.11.03.02.05.02.002 MTH.C.11.03.02.05.02.004 TOP: 9-1 The Pythagorean Theorem KEY: Pythagorean Theorem side length Pythagorean triple 4. NS:, Hypotenuse Divide both sides by 2. PTS: 1 DIF: 2 REF: 1b046606-4683-11df-9c7d-001185f0d2ea OJ: 9-2.3 Finding Side Lengths in a 30-60-90 Triangle ST: MCC9-12.G.SRT.6 LOC: MTH.C.11.03.02.05.03.001 MTH.C.11.03.02.05.03.002 TOP: 9-2 pplying Special Right Triangles KEY: special right triangles 30-60-90 5. NS: cos X = cos X = The cosine of an is. PTS: 1 DIF: 1 REF: 1bc0c06a-4683-11df-9c7d-001185f0d2ea OJ: 10-1.1 Finding Trigonometric Ratios NT: NT.CCSS.MTH.10.9-12.G.SRT.6 ST: MCC9-12.G.SRT.6 LOC: MTH.C.14.02.01.002 MTH.C.14.02.02.004 TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry cosine 6. NS: sin 79 = 0.98, cos 47 = 0.68, tan 77 = 4.33 Make sure your calculator is in degree mode. sin 79 = 0.98, cos 47 = 0.68, tan 77 = 4.33 PTS: 1 DIF: 1 REF: 1bc349d6-4683-11df-9c7d-001185f0d2ea OJ: 10-1.3 Calculating Trigonometric Ratios NT: NT.CCSS.MTH.10.K-12.5.1 TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry cosine sine tangent 7. NS: sin 49 = 0.75, cos 50 = 0.64, tan 45 = 1 Make sure your calculator is in degree mode. sin 49 = 0.75, cos 50 = 0.64, tan 45 = 1 PTS: 1 DIF: 1 REF: 1bc349d6-4683-11df-9c7d-001185f0d2ea
OJ: 10-1.3 Calculating Trigonometric Ratios NT: NT.CCSS.MTH.10.K-12.5.1 TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry cosine sine tangent 8. NS: GH = 22.46 in. GH is the length of the hypotenuse of the triangle. You are given FH, which is adjacent to. Since the adjacent side and hypotenuse are involved, use the cosine ratio. Write a trigonometric ratio. Substitute the given values. Multiply both sides by GH and divide by cos 35. in Simplify the expression. PTS: 1 DIF: 2 REF: 1bc58522-4683-11df-9c7d-001185f0d2ea OJ: 10-1.4 Using Trigonometric Ratios to Find Lengths ST: MCC9-12.G.SRT.8 TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry side length 9. NS: 10.82 feet 2.8 ft C feet Write a trigonometric ratio. Substitute the given values. Multiply both sides by and divide by sin 15. Simplify the expression. PTS: 1 DIF: 2 REF: 1bc7e77e-4683-11df-9c7d-001185f0d2ea OJ: 10-1.5 Problem-Solving pplication NT: NT.CCSS.MTH.10.9-12.G.SRT.8 ST: MCC9-12.G.SRT.8 TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry side length 10. NS: sin = 45 28 ; cos = 53 53 sin = 28 45 ; cos = 53 53
PTS: 1 DIF: 1 REF: 91632d45-6ab2-11e0-9c90-001185f0d2ea OJ: 10-1-Ext.1 Finding the Sine and Cosine of cute ngles NT: NT.CCSS.MTH.10.9-12.G.SRT.7 ST: MCC9-12.G.SRT.7 TOP: 10-1-Ext Trigonometric Ratios and Complementary ngles KEY: right triangle trigonometry sine cosine tangent 11. NS: sin = 119 120 ; cos = 169 169 sin = 120 119 ; cos = 169 169 PTS: 1 DIF: 1 REF: 91632d45-6ab2-11e0-9c90-001185f0d2ea OJ: 10-1-Ext.1 Finding the Sine and Cosine of cute ngles NT: NT.CCSS.MTH.10.9-12.G.SRT.7 ST: MCC9-12.G.SRT.7 TOP: 10-1-Ext Trigonometric Ratios and Complementary ngles KEY: right triangle trigonometry sine cosine tangent 12. NS: sin 74 PTS: 1 DIF: 2 REF: 91635455-6ab2-11e0-9c90-001185f0d2ea OJ: 10-1-Ext.2 Writing Sine in Cosine Terms and Cosine in Sine Terms NT: NT.CCSS.MTH.10.9-12.G.SRT.7 ST: MCC9-12.G.SRT.7 TOP: 10-1-Ext Trigonometric Ratios and Complementary ngles KEY: right triangle trigonometry cosine sine DOK: DOK 1 13. NS: cos 16 PTS: 1 DIF: 2 REF: 91635455-6ab2-11e0-9c90-001185f0d2ea OJ: 10-1-Ext.2 Writing Sine in Cosine Terms and Cosine in Sine Terms NT: NT.CCSS.MTH.10.9-12.G.SRT.7 ST: MCC9-12.G.SRT.7 TOP: 10-1-Ext Trigonometric Ratios and Complementary ngles KEY: right triangle trigonometry cosine sine DOK: DOK 1 14. NS: 2 Since, 2 is. Sine is the ratio of the opposite leg to the hypotenuse. 1.2 is the length of the leg opposite. 1.3 is the length of the hypotenuse. 0.5 is the length of the leg adjacent. 1.3 is the length of the hypotenuse. PTS: 1 DIF: 2 REF: 1bc80e8e-4683-11df-9c7d-001185f0d2ea OJ: 10-2.1 Identifying ngles from Trigonometric Ratios ST: MCC9-12.G.SRT.8 LOC: MTH.C.14.02.03.002 MTH.C.14.02.001 TOP: 10-2 Solving Right Triangles KEY: trigonometric ratio trigonometry 15. NS: = 44.4, = 72.5, = 88.5 Change your calculator to degree mode. Use the inverse trigonometric functions on your calculator to find each angle measure.
PTS: 1 DIF: 1 REF: 1bca49da-4683-11df-9c7d-001185f0d2ea OJ: 10-2.2 Calculating ngle Measures from Trigonometric Ratios NT: NT.CCSS.MTH.10.9-12.F.TF.7 ST: MCC9-12.G.SRT.8 LOC: MTH.C.14.04.01.002 MTH.C.14.04.02.002 MTH.C.14.04.03.002 TOP: 10-2 Solving Right Triangles KEY: trigonometric ratio trigonometry inverse trigonometric ratio DOK: DOK 1 16. NS: = 0.45 y the Pythagorean Theorem,. PTS: 1 DIF: 2 REF: 1bccac36-4683-11df-9c7d-001185f0d2ea OJ: 10-2.3 Solving Right Triangles ST: MCC9-12.G.SRT.8 LOC: MTH.C.14.02.02.002 TOP: 10-2 Solving Right Triangles KEY: trigonometric ratio trigonometry solve right triangles 17. NS: ngles of elevation: 1, 3 ngles of depression: 2, 4 1 and 3 are formed by a horizontal line and a line of sight to a point above the line. They are angles of elevation. 2 and 4 are formed by a horizontal line and a line of sight to a point below the line. They are angles of depression. PTS: 1 DIF: 1 REF: 1bd170ee-4683-11df-9c7d-001185f0d2ea OJ: 10-3.1 Classifying ngles of Elevation and Depression ST: MCC9-12.G.SRT.8 LOC: MTH.C.11.02.04.10.001 MTH.C.11.02.04.10.002 TOP: 10-3 ngles of Elevation and Depression KEY: angle of elevation angle of depression trigonometry DOK: DOK 1 18. NS: 402 m 146.2 m 20º x Use the side opposite and x, and the side adjacent to to write the tangent ratio. Multiply both sides by x and divide both sides by. Simplify. PTS: 1 DIF: 2 REF: 1bd197fe-4683-11df-9c7d-001185f0d2ea
OJ: 10-3.2 Finding Distance by Using ngle of Elevation NT: NT.CCSS.MTH.10.9-12.G.SRT.8 ST: MCC9-12.G.SRT.8 TOP: 10-3 ngles of Elevation and Depression KEY: angle of elevation angle of depression trigonometry 19. NS: 1,120 ft R 15º 300 ft x 15º S y the lternate Interior ngles Theorem, m. From the sketch,. So. PTS: 1 DIF: 2 REF: 1bd3d34a-4683-11df-9c7d-001185f0d2ea OJ: 10-3.3 Finding Distance by Using ngle of Depression NT: NT.CCSS.MTH.10.9-12.G.SRT.8 ST: MCC9-12.G.SRT.8 TOP: 10-3 ngles of Elevation and Depression KEY: angle of elevation angle of depression trigonometry 20. NS: 1.2 km 1.8 km 23 D 23 C Step 1 Draw a sketch. Let and C represent the beginning and end of the runway. Let C be the length of the runway. Step 2 Find. y the lternate Interior ngles Theorem, m. In, So Step 3 Find. y the lternate Interior ngles Theorem, m. In, So Step 4 Find. So the runway is about 1.2 km long. PTS: 1 DIF: 2 REF: 1bd3fa5a-4683-11df-9c7d-001185f0d2ea
OJ: 10-3.4 pplication NT: NT.CCSS.MTH.10.9-12.G.SRT.8 ST: MCC9-12.G.SRT.8 TOP: 10-3 ngles of Elevation and Depression KEY: angle of elevation angle of depression trigonometry