Assignment Guide: Chapter 8 Geometry (L3) (91) 8.1 The Pythagorean Theorem and Its Converse Page 495-497 #7-31 odd, 37-47 odd (92) 8.2 Special Right Triangles Page 503-504 #7-12, 15-20, 23-28 (93) 8.2 Special Right Triangles Worksheets (in assignment guide, pages 9-10) (94) 8.2 Special Right Triangles Page 514 #1-16 Worksheets (in assignment guide, page 11) Study for quiz (8.1 8.2) (95) Quiz: Sections 8.1 8.2 Page 505 #34-43 Bring a scientific calculator for the net lesson (96) 8.3 Trigonometry Page 510-511 #1-8, 11-19, 22-27, 33-35 (97) 8.3 Trigonometry Worksheets (in assignment guide, page 14) (98) 8.3 Trigonometry Worksheets (in assignment guide, page 15) (99) 8.4 Angles of Elevation and Depression Page 519-521 #17-23, 33, 36 (100) 8.4 Angles of Elevation and Depression Worksheets (in assignment guide, page 17) (101) Review: 8.3 8.4 Worksheets (in assignment guide, pages 18-19) Study for quiz (8.3 8.4) (102) Quiz: Sections 8.3 8.4 Worksheets (in assignment guide, pages 20-22) (103) Review: Chapter 8 Page 537 #1-24 Study for Test (Chapter 8) (104) TEST: Chapter 8 Page 537 #1-24 This is a guide. Homework is subject to change. Check the chalkboard in class for updates and/or changes. 0
Geometry Notes, Section 8.1 The Pythagorean Theorem & Its Converse Parts of a right triangle: a and b are called the c is the and y are angles Pythagorean Theorem: If the triangle is right, then. Try these: Find the value of in each right triangle. 1. 2. 3. Converse of the Pythagorean Theorem: If a 2 + b 2 = c 2, then the triangle is. Try these: Which of the following triangles are right triangles? 4. 5. 6. 7 9 16 25 12 24 9 5 6 Pythagorean Triple: A set of nonzero whole numbers, a, b, and c that satisfy the equation a 2 + b 2 = c 2. If you multiply each number in a Pythagorean triple by the same whole number, the three numbers that result also form a Pythagorean triple. Some common Pythagorean Triples: (MEMORIZE!) 3, 4, 5 6, 8, 10 9, 12, 15 12, 16, 20 15, 20, 25 5, 12, 13 10, 24, 26 8, 15, 17 7, 24, 25 1
Pythagorean Inequalities: If c 2 > a 2 + b 2, then the triangle is. If c 2 < a 2 + b 2, then the triangle is. Classifying Acute and Obtuse Triangles compare 2 c with a b ; c is always the LARGEST side. 2 2 2 2 2 2 Right triangle: c a b Acute triangle: c a b Obtuse triangle: c a b 2 2 2 2 2 Try these: Tell whether a triangle with the given sides is right, obtuse, or acute. 1. 12, 14, 15 2. 5, 5, 5 3. 3, 4, 7 Pythagorean Theorem Word Problems: Draw a picture, then use the Pythagorean Theorem to solve the problems. 4. The size of a computer monitor is the length of its diagonal. You want to buy a 19-in. monitor that has a height of 11 in. What is the width of the monitor? Round to the nearest tenth of an inch. 5. A si-foot-long ladder leans against a building. If the base of the ladder is four feet from the wall, how far up the wall does the ladder reach? Round to the nearest tenth of a foot. 6. Jill s front door is 42 wide and 84 tall. She purchased a circular table that is 96 inches in diameter. Will the table fit through the front door? 7. A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance? 2
Geometry Practice, Section 8.1 The Pythagorean Theorem & Its Converse 3
Geometry Practice, Section 8.1 The Pythagorean Theorem & Its Converse For all word problems, find a decimal approimation 2 decimal places. 1. A 48-inch wide screen TV means that the measure along the diagonal is 48 inches. If the screen is square, what are the dimensions of the length and width? 1 2. The doorway of the family room measures 6 2 feet by 3 feet. What is the length of the diagonals of the doorway? 3. You place a 10-foot ladder against a wall. If the base of the ladder is 3 feet from the wall, how high up the wall does the top of the ladder reach? 4. The minute hand of Big Ben is 14 feet long and the hour hand is 9 feet long. What is the distance between the tips of the hands at 3:00 pm? 5. The N S distance from South Bend to Indianapolis is about 140 miles. Richmond is about 73 miles due East of Indianapolis. What is the distance between South Bend and Richmond as the crow flies? 6. Four guide wires are to be placed from the top of a 40 meter tall radio tower to points 12 meters from the center of the base of the tower. What is the total length of wire needed? 7. The glass for a window is 7.5 feet wide. About how high must a 3 feet wide doorway be in order for a contractor to get the glass through the door? (hint: angle the glass diagonally through the door) 8. The trunk of a 36 foot tree is broken part way from the base of the tree to the top. Although the top is still partially attached, it falls and just touches the ground 12 feet from the base of the tree. How much of the tree is still standing? 4
10. A smaller commuter airline flies to three cities whose locations for the vertices of a right triangle. The total flight distance (from city A to city B to city C and back to City A) is 1400 miles. It is 600 miles between the two cities that are furthest apart. Find the other two distances between cities. 11. Each base on a standard baseball diamond lies 90 feet from the net. Find the distance the catcher must throw a baseball from 3 feet behind home plate to second base. 5
Geometry Notes, Section 8.2 Special Right Triangles 45-45 -90 Triangle Theorem: In a 45-45 -90 triangle, both legs are congruent and the length of the hypotenuse is times the length of a leg Hypotenuse = leg Try these: Solve the following problems using special right triangles. 1. Find the value of. 2. What is the length of the hypotenuse of a 45-45 - 90 triangle with leg length? 5 3 3. The length of the hypotenuse of a 45-45 -90 triangle is 10. What is the length of one leg? 4. You plan to build a path along one diagonal of a 100 ft-by-100 ft square garden. To the nearest foot how long with the path be? 30-60 -90 Triangle Theorem: In a 30-60 -90 triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is times the length of the shorter leg. Hypotenuse = shorter leg Longer leg = shorter leg Try these: Solve the following problems using special right triangles. 5. Find the value of. 6. An artisan makes pendants in the shape of 12 equilateral triangles. Suppose the sides of a pendant 60 are 18 mm long. What is the height of the pendant to the nearest tenth of a millimeter? 6
Geometry Practice, Section 8.2 Special Right Triangles (45-45-90 triangles) 45 2 45 Solve for all missing sides in each triangle. 1. Given: leg Now you try! 12 6 2. Given: hypotenuse with 2 6 2 10 2 3. Given: hypotenuse with (not 2 ) 5 6 9 10 4. Given: whole-number hypotenuse 8 12 7
Geometry Practice, Section 8.2 Special Right Triangles (30-60-90 triangles) 60 2 Always find the short side first! 3 30 Solve for all missing sides in each triangle. 5. Given: short side (across from 30 angle) Now you try! 60 60 6 8 30 30 6. Given: hypotenuse 60 8 60 4 30 30 7. Given: long side (across from 60 angle) with 3 60 60 30 30 10 3 5 3 8. Given: whole-number long side (across from 60 angle) 60 60 30 30 6 10 8
Geometry Homework, Section 8.2 Special Right Triangles Complete the table. Complete the table. 9
Geometry Homework, Section 8.2 Special Right Triangles 10
Geometry Practice, Sections 8.1-8.2 11
Geometry Notes, Section 8.3 Sine, Cosine, and Tangent Trigonometry: Greek, meaning triangle measurement There are 3 ratios that are calculated using the side lengths of right triangles. However, the ratios depend on the size of the angle, not on the size of the triangle itself. Memory trick: SOH CAH TOA opposite sin hypotenuse adjacent cos hypotenuse opposite tan adjacent S C T O H A H O A SOH CAH TOA Finding missing SIDES: set up the ratio; use the sin, cos, or tan button on your calculator 1. 2. 3. 3 5 7 27 42 16 4. 5. 6. 8 6 33 4 51 22 Finding missing ANGLES: set up the ratio; use the 1 1 1 sin, cos, or tan button on your calculator 7. 8. 9. 1 18 4 7 15 13 10. 11. 12. 10 19 6 4 5 3 12
Geometry Practice, Section 8.3 Sine, Cosine, and Tangent Complete. Use a scientific calculator or the table on the last page of your packet. Use a scientific calculator or the table on the last page of your packet to find the values of the variables. Find lengths correct to the nearest integer and angles to the nearest degree. 13
Geometry Homework, Sections 8.3 Sine, Cosine, and Tangent 14
Geometry Homework, Sections 8.3 Sine, Cosine, and Tangent Find the measure of the indicated angle to the nearest degree. Use sin -1, cos -1, or tan -1 when needed. 1. sin B = 0.4848 2. cos A = 0.6157 3. tan W = 19.0811 4. cos A = 0.7431 5. tan B = 0.5317 6. sin A = 0.5150 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 15
Geometry Notes, Section 8.4 Applications of Right Triangle Trig Angle of Elevation looking up from horizontal Angle of Depression looking down from horizontal 1. A sonar operator on a ship detects a submarine at a distance of 400 meters and an angle of depression of 35. How deep is the submarine? 2. You lean a 16 foot ladder against the wall. If the base is 4 feet from the wall, what angle does the ladder make with the ground? 3. A ramp was built by the loading dock. The height of the loading platform is 4 feet. Determine the length of the ramp if it has an angle of elevation of 32. 4. The angle of depression from the top of a 320 foot office building to the top of a 200 foot office building is 55. How far apart are the two buildings? 5. A person standing 30 feet from a flagpole can see the top of the pole at a 35 angle of elevation. a. Draw a diagram. b. The person s eye level is 5 ft from the ground. Find the height of the flagpole to the nearest foot. 16
Geometry Practice, Section 8.4 Applications of Right Triangle Trig 17
Geometry Review 8.3 8.4 Review Use a scientific calculator or the table on the last page of your packet to complete the following statements. Use a scientific calculator or the table on the last page of your packet to find the values of the variables. Find lengths correct to the nearest integer and angles to the nearest degree. 18
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Geometry Review, Chapter 8 Test Review Find the value of. 1. 2. 3. 9 13 5 16 12 25 4. 5. 6. 12 5 8 16 5 12 7. A rectangle has length 2.4 m and width 0.7 m. Find the length of a diagonal. 8. A square has perimeter 12 cm. Find the length of a diagonal. 9. The diagonals of a rhombus have lengths 12 and 16. Find the perimeter of the rhombus. 20
Find the value of. 10. 11. 12. 10 6 9 60 11 5 13. 14. 15. 60 6 45 10 Use a calculator to find the value of. Find lengths correct to the nearest integer, and angles correct to the nearest degree. 16. 17. 18. 25 43 9 13 65 10 21
Find the length of each segment. 19. The hypotenuse of a right triangle with legs of lengths 5 and 12 20. A diagonal of a rectangle with width 7 cm and length 24 cm 21. A diagonal of a square with sides of length 12 22. The altitude to the base of an isosceles triangle with sides of lengths 12, 12, and 20 Tell whether the triangle with sides of the given lengths is acute, right, or obtuse. 23. 7, 7, 10 24. 6, 7, 8 25. 1, 2.4, 2.6 Find the value of each variable. 26. 27. y z 12 16 30 14 y Find the value of correct to the nearest integer. 28. 29. 30. 26 24 32 62 35 42 22
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