Unit 2 Review. Short Answer 1. Find the value of x. Express your answer in simplest radical form.
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1 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 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 in. H
2 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 cm cm 15. Use your calculator to find the angle measures to the nearest tenth of a degree. 16. Find to the nearest hundredth C 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 The largest Egyptian pyramid is 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 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.
3 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 df-9c7d f0d2ea OJ: Using the Pythagorean Theorem ST: MCC9-12.G.SRT.8 LOC: MTH.C MTH.C 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: 1afadc df-9c7d f0d2ea OJ: pplication NT: NT.CCSS.MTH G.SRT.8 ST: MCC9-12.G.SRT.8 LOC: MTH.C MTH.C 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.
4 The side lengths are nonzero whole numbers that satisfy the equation triple., so they form a Pythagorean PTS: 1 DIF: 1 REF: 1afd3ef df-9c7d f0d2ea OJ: Identifying Pythagorean Triples ST: MCC9-12..REI.4b LOC: MTH.C MTH.C 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: 1b df-9c7d f0d2ea OJ: Finding Side Lengths in a Triangle ST: MCC9-12.G.SRT.6 LOC: MTH.C MTH.C TOP: 9-2 pplying Special Right Triangles KEY: special right triangles NS: cos X = cos X = The cosine of an is. PTS: 1 DIF: 1 REF: 1bc0c06a df-9c7d f0d2ea OJ: Finding Trigonometric Ratios NT: NT.CCSS.MTH G.SRT.6 ST: MCC9-12.G.SRT.6 LOC: MTH.C MTH.C 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: 1bc349d df-9c7d f0d2ea OJ: Calculating Trigonometric Ratios NT: NT.CCSS.MTH.10.K 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: 1bc349d df-9c7d f0d2ea
5 OJ: Calculating Trigonometric Ratios NT: NT.CCSS.MTH.10.K TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry cosine sine tangent 8. NS: GH = 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: 1bc df-9c7d f0d2ea OJ: 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: 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 df-9c7d f0d2ea OJ: Problem-Solving pplication NT: NT.CCSS.MTH G.SRT.8 ST: MCC9-12.G.SRT.8 TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry side length 10. NS: sin = ; cos = sin = ; cos = 53 53
6 PTS: 1 DIF: 1 REF: 91632d45-6ab2-11e0-9c f0d2ea OJ: 10-1-Ext.1 Finding the Sine and Cosine of cute ngles NT: NT.CCSS.MTH 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 = ; cos = sin = ; cos = PTS: 1 DIF: 1 REF: 91632d45-6ab2-11e0-9c f0d2ea OJ: 10-1-Ext.1 Finding the Sine and Cosine of cute ngles NT: NT.CCSS.MTH 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: ab2-11e0-9c f0d2ea OJ: 10-1-Ext.2 Writing Sine in Cosine Terms and Cosine in Sine Terms NT: NT.CCSS.MTH 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 NS: cos 16 PTS: 1 DIF: 2 REF: ab2-11e0-9c f0d2ea OJ: 10-1-Ext.2 Writing Sine in Cosine Terms and Cosine in Sine Terms NT: NT.CCSS.MTH 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 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 df-9c7d f0d2ea OJ: Identifying ngles from Trigonometric Ratios ST: MCC9-12.G.SRT.8 LOC: MTH.C MTH.C 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.
7 PTS: 1 DIF: 1 REF: 1bca49da df-9c7d f0d2ea OJ: Calculating ngle Measures from Trigonometric Ratios NT: NT.CCSS.MTH F.TF.7 ST: MCC9-12.G.SRT.8 LOC: MTH.C MTH.C MTH.C TOP: 10-2 Solving Right Triangles KEY: trigonometric ratio trigonometry inverse trigonometric ratio DOK: DOK NS: = 0.45 y the Pythagorean Theorem,. PTS: 1 DIF: 2 REF: 1bccac df-9c7d f0d2ea OJ: Solving Right Triangles ST: MCC9-12.G.SRT.8 LOC: MTH.C 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 df-9c7d f0d2ea OJ: Classifying ngles of Elevation and Depression ST: MCC9-12.G.SRT.8 LOC: MTH.C MTH.C TOP: 10-3 ngles of Elevation and Depression KEY: angle of elevation angle of depression trigonometry DOK: DOK NS: 402 m 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 df-9c7d f0d2ea
8 OJ: Finding Distance by Using ngle of Elevation NT: NT.CCSS.MTH 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 df-9c7d f0d2ea OJ: Finding Distance by Using ngle of Depression NT: NT.CCSS.MTH 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 df-9c7d f0d2ea
9 OJ: pplication NT: NT.CCSS.MTH 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
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