Use the figure on the right to answer the following questions. 1. 𝑈𝑆 is the geometric mean between _______ and _______. 2. 𝑅𝑈 is the geometric mean between _______ and _______. 3. 𝑈𝑇 is the geometric mean between _______ and _______. Use geometric means to solve for the following variables. 4. x = ____________ y = ____________ z = ____________ 5. x = ____________ y = ____________ z = ____________ w = ____________
Geometry – Right Triangles and Trigonometry Chapter Test Review
Use the Pythagorean theorem to solve for the missing side length. 6. 7. Tell whether a triangle formed with sides having the lengths named below is acute, obtuse, right, or does not exist. 8. 6, 15, 9 9. 7, 15, 20 10. 43, 29, 38 11. 24, 45, 51 Use properties of special triangles to find the missing side lengths. You will lose credit if you use any other method. 12. 13.
Use trigonometry to solve for each variable. 23. Solve each of the following. You must include a diagram with each problem. 24. You are flying a kite and have let out 250 feet of string. The angle of elevation is 52º. If the kite is directly above your house, how far are you from the house? 25. You are standing at the top of a building. As you look across the street to another building, the angle of depression to the bottom is 58º. If the buildings are 280 feet apart from each other, how tall is the building that you are in?
Use the Laws of Sines or the Law of Cosines to solve for each variable. 26. 27. Completely solve the triangle using the Laws of Sines and the Law of Cosines. 28. AB = ____________ ∠A = ____________ BC = ____________ ∠B = ____________ AC = ____________ ∠C = ____________
Use the figure on the right to answer the following questions. 1. 𝑅𝑇 is the geometric mean between _______ and _______. 2. 𝑋𝑅 is the geometric mean between _______ and _______. 3. 𝑅𝑍 is the geometric mean between _______ and _______. Use geometric means to solve for the following variables. 4. x = ____________ y = ____________ z = ____________ 5. x = ____________ y = ____________ z = ____________ w = ____________
Geometry – Right Triangles and Trigonometry Chapter Test
Use the Pythagorean theorem to solve for the missing side length. 6. 7. Tell whether a triangle formed with sides having the lengths named below is acute, obtuse, right, or does not exist. 8. 23, 53, 39 9. 16, 29, 32 10. 36, 77, 85 11. 31, 63, 24 Use properties of special triangles to find the missing side lengths. You will lose credit if you use any other method. 12. 13.
Use trigonometry to solve for each variable. 23. Solve each of the following. You must include a diagram with each problem. 24. A water tower casts a shadow that is 150 feet long. You stand at the end of the shadow and measure the angle of elevation to be 38º. What is the height of the tower? 25. You are shooting a cannonball during a war reenactment. To make sure the cannonball hits the target, you must set the angle of the cannon correctly. If the cannon is fifty feet away from a thirty-‐foot tall target, what angle of elevation should you set the cannon for?
Use the Laws of Sines or the Law of Cosines to solve for each variable. 26. 27. Completely solve the triangle using the Laws of Sines and the Law of Cosines. 28. AB = ____________ ∠A = ____________ BC = ____________ ∠B = ____________ AC = ____________ ∠C = ____________
Bonus: Solve for the following variables. A = ____________ E= ____________ B = ____________ F = ____________ C = ____________ G = ____________ D = ____________ H = ____________ Bonus: Solve for x.
Use the figure on the right to answer the following questions. 1. 𝑀𝑃 is the geometric mean between _______ and _______. 2. 𝑄𝑀 is the geometric mean between _______ and _______. 3. 𝑀𝑅 is the geometric mean between _______ and _______. Use geometric means to solve for the following variables. 4. x = ____________ y = ____________ z = ____________ 5. x = ____________ y = ____________ z = ____________ w = ____________
Geometry – Right Triangles and Trigonometry Chapter Test
Use the Pythagorean theorem to solve for the missing side length. 6. 7. Tell whether a triangle formed with sides having the lengths named below is acute, obtuse, right, or does not exist. 8. 28, 45, 53 9. 21, 36, 30 10. 27, 49, 20 11. 35, 42, 65 Use properties of special triangles to find the missing side lengths. You will lose credit if you use any other method. 12. 13.
Use trigonometry to solve for each variable. 23. Solve each of the following. You must include a diagram with each problem. 24. A water tower casts a shadow that is 320 feet long. You stand at the end of the shadow and measure the angle of elevation to be 22º. What is the height of the tower? 25. You are shooting a cannonball during a war reenactment. To make sure the cannonball hits the target, you must set the angle of the cannon correctly. If the cannon is sixty feet away from a twenty-‐foot tall target, what angle of elevation should you set the cannon for?
Use the Laws of Sines or the Law of Cosines to solve for each variable. 26. 27. Completely solve the triangle using the Laws of Sines and the Law of Cosines. 28. AB = ____________ ∠A = ____________ BC = ____________ ∠B = ____________ AC = ____________ ∠C = ____________
Bonus: Solve for the following variables. A = ____________ E= ____________ B = ____________ F = ____________ C = ____________ G = ____________ D = ____________ H = ____________ Bonus: Solve for x.
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