G.8 Right Triangles STUDY GUIDE Name Date Block Chapter 7 Right Triangles Review and Study Guide Things to Know (use your notes, homework, quizzes, textbook as well as flashcards at quizlet.com (http://quizlet.com/4216735/geometry-chapter-7-right-triangles-flashcardsflash-cards/)). DO NOT LIMIT YOUR STUDYING TO PROBLEMS IN THIS STUDY GUIDE! Pythagorean Theorem: a 2 + b 2 = c 2, where a and b are legs and c is the hypotenuse. If a 2 + b 2 = c 2, then the triangle is right If a 2 + b 2 < c 2, then the triangle is obtuse If a 2 + b 2 > c 2, then the triangle is acute Some Pythagorean Triples to know: 3, 4, 5; 5, 12, 13; 8, 15, 17 If the altitude is drawn to the hypotenuse of a right triangle, similar triangles are formed, with geometric mean relationships: o CD = o CB = o AC = AD BD BD AB AD AB In a 45 o -45 o -90 o triangle (an isosceles right triangle), the legs are congruent, and the hypotenuse = leg* 2 In a 30 o -60 o -90 o triangle, the hypotenuse is 2*shorter leg (side opposite the 30 o angle), and the longer leg (side opposite the 60 o angle) = shorter leg* 3 Trigonometric ratios (SOH CAH TOA): opp adj opp o sin = ; cos = ; tan = hyp hyp adj o Use to find missing sides in right triangles, given an angle and a side Angle of elevation / angle of depression o elevation: angle formed when you look up from the horizontal o depression: angle formed when you look down from the horizontal o be able to solve word problems using angle of elevation or depression Inverse trigonometric functions: o Tell us: angle whose sin/cos/tan is <ratio measure>. o Use to find missing angles in right triangles Solving a triangle o Find missing angles and sides of a right triangle o Use Pythagorean Theorem, Triangle Sum Theorem and corollary (given one acute angle of a right triangle, find the other by subtracting it from 90), trig ratios, and inverse trig ratios Word problems: be able to interpret word problems (draw picture!) to find missing angles or sides
G.8 Right Triangles STUDY GUIDE Page 2 Example problems: 1) Find sin A, cos A, and tan A. 2) Find x in simplest radical form. 3) Find x in simplest radical form. 4) Classify the triangle is acute, right, or obtuse: a) 12, 14, 18 b) 9, 15, 3 34 c) 12, 15, 3 40 d) 10, 13, 5 12 5) Find the values of the variables in simplest radical form. c) 6) Find the value of the variables in simplest radical form. c) d)
G.8 Right Triangles STUDY GUIDE Page 3 7) What is the value of z? 8) Find the value of x to the nearest tenth. c) d) 9) Solve the right triangles (round to nearest tenth if necessary): c) d) 10) A 50 foot tree casts a shadow of length 60 feet. To the nearest tenth, what is the angle of elevation of the tree with respect to the ground?
G.8 Right Triangles STUDY GUIDE Page 4 11) A bird sits on top of a lamppost. The angle of depression from the bird to the feet of an observer standing away from the lamppost is 35 o. The distance from the bird to the observer is 25 meters. To the nearest tenth, how tall is the lamppost? 12) Kyle got his kite stuck in a tree. The kite s string is 180 feet long. He is standing 80 feet away from the tree. To the nearest foot, how tall is the tree? 13) A model baseball diamond (which is actually a square) has a distance from 1 st base to 3 rd base that measures 14 cm. To the nearest tenth, find the lengths between 3 rd base and home plate. 14) An 8 meter telephone pole has a support wire that is secured from the top of the pole to the ground. The support wire measures 15 meters. a) What angle of elevation, to the nearest tenth, does the wire make with the ground (assume the ground is level)? b) How far is the bottom of the pole from the wire (to the nearest tenth)? 15) Fill in the missing values in the tables.
G.8 Right Triangles STUDY GUIDE Page 5 16) Triangle ABC is an equilateral triangle with side lengths 10 inches. What is AD? 17) A ladder 12 meters long leans against a building. It rests on the wall at a point 10 meters above the ground. Find the angle (to the nearest degree) the ladder makes with the ground. 18) From a point 12 feet from the base of a building, the angle of elevation from the ground to the top of the building is 70 o. To the nearest foot, what is the height of the building? 19) Bob needs to build a bridge to go across a pond. He has been able to collect the measurements as shown in the diagram. About (to the nearest foot) how long does his bridge need to be? 20) From a cliff 140 feet above the shore line, an observer notes that the angle of depression of a ship is 21 o. Find the distance from the ship to a point on the shore directly below the observer.
G.8 Right Triangles STUDY GUIDE Page 6 Answers 5 12 5 1) sin A, cos A, tan A 13 13 12 2) 2 29 3) 90 4) a) acute b) right c) acute d) obtuse 5) a) x= 4 3 b) x=5 c) a = 15; b = 16; c = 20 6) a) x=9, y= 9 3 b) x= 6 2, y=6 c) x = 6 3 ; y = 3 d) x = 7; y = 2 7) 4 2 8) a) 5.1 b) 14.0 c) 4.8 cm d) 68.6 9) a) AB 9.7; A 35.7; C 54.3 b) G 28.6 ; EG 16.5; EF 7.9 c) B 53, AC=57.1, AB=71.5 d) A 38.7, B 51.3, AB=6.2 10) 39.8 o 11) 14.3 m 12) 161 ft 13) 9.9 cm 14) a) 32.2 o b) 12.7 m 15) a) b) 16) 5 3inches 17) 56 o 18) 33 ft 19) 12 ft 20) 365 ft