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New SAT Math Workbook Episode 2 part 3

Tham khảo tài liệu 'new sat math workbook episode 2 part 3', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Geometry 205 3. RIGHT TRIANGLES A. Pythagorean theorem leg 2 leg 2 hypotenuse 2 5 2 2 2 X2 25 4 X2 29 X2 X 729 B. Pythagorean triples These are sets of numbers that satisfy the Pythagorean Theorem. When a given set of numbers such as 3 4 5 forms a Pythagorean triple 32 42 52 any multiples of this set such as 6 8 10 or 30 40 50 also form a Pythagorean triple. Memorizing the sets of Pythagorean triples that follow will save you valuable time in solving problems for if you recognize given numbers as multiples of Pythagorean triples you do not have to do any arithmetic at all. The most common Pythagorean triples that should be memorized are 3 4 5 5 12 13 8 15 17 7 24 25 Squaring 34 and 16 to apply the Pythagorean theorem would take too much time. Instead recognize the hypotenuse as 2 17 . Suspect an 8 15 17 triangle. Since the given leg is 2 8 the missing leg will be 2 15 or 30 without any computation at all. www.petersons.com 206 Chapter 13 C. 30 -60 -90 triangle a The leg opposite the 30 angle is one-half the hypotenuse. b The leg opposite the 60 angle is one-half the hypotenuse 5 3 . c An altitude in an equilateral triangle forms a 30 -60 -90 triangle and is therefore equal to one-half the side V3 . D. 45 -45 -90 triangle isosceles right triangle a Each leg is one-half the hypotenuse times V2 . b Hypotenuse is leg times V2 . c The diagonal of a square forms a 45 -45 -90 triangle and is therefore equal to a side times V2 . www.petersons.com Geometry 207 Exercise 3 Work out each problem. Circle the letter that appears before your answer. 1. A farmer uses 140 feet of fencing to enclose a rectangular field. If the ratio of length to width is 3 4 find the diagonal in feet of the field. A 50 B 100 C 20 D 10 E cannot be determined 2. Find the altitude of an equilateral triangle whose side is 20. A B C D E 10 20 3 10 3 20 2 10V2 3. Two boats leave the same dock at the same time one traveling due west at 8 miles per hour and the other due north at 15 miles per hour. How many