Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
4th Edition
ISBN: 9780134686974
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Chapter 7.4, Problem 51AYU

Perfect Triangles A perfect triangle is one having integers for sides for which the area is numerically equal to the perimeter. Show that the triangles with the given side lengths are perfect.

(a) 9, 10, 17

(b) 6, 25, 29

Source: M.V. Bonsangue, G. E. Gannon, E. Buchman, and N. Gross, “In Search of Perfect Triangles,� Mathematics Teacher, Vol. 92, No. 1, 1999: 56-61

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Chapter 7 Solutions

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

Ch. 7.1 - In a right triangle, if the length of the...Ch. 7.1 - Prob. 2AYUCh. 7.1 - Prob. 3AYUCh. 7.1 - Prob. 4AYUCh. 7.1 - Prob. 5AYUCh. 7.1 - Prob. 6AYUCh. 7.1 - True or False In a right triangle, if two sides...Ch. 7.1 - Prob. 8AYUCh. 7.1 - In Problems 9-18, find the exact value of the six...Ch. 7.1 - Prob. 10AYU
Ch. 7.1 - Prob. 11AYUCh. 7.1 - Prob. 12AYUCh. 7.1 - Prob. 13AYUCh. 7.1 - Prob. 14AYUCh. 7.1 - Prob. 15AYUCh. 7.1 - Prob. 16AYUCh. 7.1 - In Problems 9-18, find the exact value of the six...Ch. 7.1 - In Problems 9-18, find the exact value of the six...Ch. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - Prob. 22AYUCh. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - Prob. 26AYUCh. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - Prob. 28AYUCh. 7.1 - In Problems 29-42, use the right triangle shown...Ch. 7.1 - Prob. 30AYUCh. 7.1 - Prob. 31AYUCh. 7.1 - Prob. 32AYUCh. 7.1 - Prob. 33AYUCh. 7.1 - In Problems 29-42, use the right triangle shown...Ch. 7.1 - Prob. 35AYUCh. 7.1 - Prob. 36AYUCh. 7.1 - In Problems 29-42, use the right triangle shown...Ch. 7.1 - Prob. 38AYUCh. 7.1 - Prob. 39AYUCh. 7.1 - Prob. 40AYUCh. 7.1 - Prob. 41AYUCh. 7.1 - Prob. 42AYUCh. 7.1 - Prob. 43AYUCh. 7.1 - Prob. 44AYUCh. 7.1 - Prob. 45AYUCh. 7.1 - Prob. 46AYUCh. 7.1 - Geometry A right triangle contains a 25 angle. (a)...Ch. 7.1 - Prob. 48AYUCh. 7.1 - Prob. 49AYUCh. 7.1 - Prob. 50AYUCh. 7.1 - Prob. 51AYUCh. 7.1 - Prob. 52AYUCh. 7.1 - Prob. 53AYUCh. 7.1 - Prob. 54AYUCh. 7.1 - Prob. 55AYUCh. 7.1 - Prob. 56AYUCh. 7.1 - Finding the Speed of a Truck A state trooper is...Ch. 7.1 - Prob. 58AYUCh. 7.1 - Prob. 59AYUCh. 7.1 - Parallax See Problem 59. 61 Cygni, sometimes...Ch. 7.1 - Prob. 61AYUCh. 7.1 - Prob. 62AYUCh. 7.1 - Prob. 63AYUCh. 7.1 - Prob. 64AYUCh. 7.1 - Prob. 65AYUCh. 7.1 - Prob. 66AYUCh. 7.1 - Constructing a Highway A highway whose primary...Ch. 7.1 - Photography A camera is mounted on a tripod 4 feet...Ch. 7.1 - Prob. 69AYUCh. 7.1 - Prob. 70AYUCh. 7.1 - Mt. Rushmore To measure the height of Lincoln’s...Ch. 7.1 - Prob. 72AYUCh. 7.1 - Chicago Skyscrapers The angle of inclination from...Ch. 7.1 - Prob. 74AYUCh. 7.1 - Prob. 75AYUCh. 7.1 - Shooting Free Throws in Basketball The eyes of a...Ch. 7.1 - Geometry Find the value of the angle in degrees...Ch. 7.1 - Surveillance Satellites A surveillance satellite...Ch. 7.1 - Prob. 79AYUCh. 7.1 - Prob. 80AYUCh. 7.1 - Explain how you would measure the height of a TV...Ch. 7.1 - The Gibb’s Hill Lighthouse, Southampton, Bermuda...Ch. 7.1 - Prob. 84AYUCh. 7.1 - Prob. 85AYUCh. 7.1 - Prob. 86AYUCh. 7.1 - Prob. 87AYUCh. 7.2 - The difference formula for the sine function is...Ch. 7.2 - Prob. 2AYUCh. 7.2 - Prob. 3AYUCh. 7.2 - Prob. 4AYUCh. 7.2 - Prob. 5AYUCh. 7.2 - Prob. 6AYUCh. 7.2 - Prob. 7AYUCh. 7.2 - Prob. 8AYUCh. 7.2 - In Problems 9-16, solve each triangle.Ch. 7.2 - Prob. 10AYUCh. 7.2 - In Problems 9-16, solve each triangle. Ch. 7.2 - Prob. 12AYUCh. 7.2 - Prob. 13AYUCh. 7.2 - Prob. 14AYUCh. 7.2 - Prob. 15AYUCh. 7.2 - Prob. 16AYUCh. 7.2 - In problems 17-24, solve each triangle....Ch. 7.2 - Prob. 18AYUCh. 7.2 - Prob. 19AYUCh. 7.2 - Prob. 20AYUCh. 7.2 - Prob. 21AYUCh. 7.2 - Prob. 22AYUCh. 7.2 - Prob. 23AYUCh. 7.2 - Prob. 24AYUCh. 7.2 - Prob. 25AYUCh. 7.2 - Prob. 26AYUCh. 7.2 - In problems 25-36, two sides and an angle are...Ch. 7.2 - Prob. 28AYUCh. 7.2 - Prob. 29AYUCh. 7.2 - Prob. 30AYUCh. 7.2 - Prob. 31AYUCh. 7.2 - Prob. 32AYUCh. 7.2 - Prob. 33AYUCh. 7.2 - Prob. 34AYUCh. 7.2 - Prob. 35AYUCh. 7.2 - Prob. 36AYUCh. 7.2 - Finding the Length of a Ski Lift Consult the...Ch. 7.2 - Finding the Height of a Mountain Use the...Ch. 7.2 - Finding the Height of an Airplane An aircraft is...Ch. 7.2 - Finding the Height of the Bridge over the Royal...Ch. 7.2 - Prob. 41AYUCh. 7.2 - Distance between Runners Two runners in a marathon...Ch. 7.2 - Prob. 43AYUCh. 7.2 - Prob. 44AYUCh. 7.2 - Prob. 45AYUCh. 7.2 - Prob. 46AYUCh. 7.2 - Rescue at Sea Coast Guard Station Able is located...Ch. 7.2 - Prob. 48AYUCh. 7.2 - Finding the Lean of the Leaning Tower of Pisa The...Ch. 7.2 - Prob. 50AYUCh. 7.2 - Constructing a Highway A highway whose primary...Ch. 7.2 - Calculating Distances at Sea The navigator of a...Ch. 7.2 - Prob. 53AYUCh. 7.2 - Prob. 54AYUCh. 7.2 - Prob. 55AYUCh. 7.2 - Prob. 56AYUCh. 7.2 - The Original Ferris Wheel George Washington Gale...Ch. 7.2 - Mollweide’s Formula For any triangle, Mollweide’s...Ch. 7.2 - Prob. 61AYUCh. 7.2 - Prob. 62AYUCh. 7.2 - Prob. 63AYUCh. 7.2 - Prob. 64AYUCh. 7.2 - Prob. 65AYUCh. 7.2 - Prob. 66AYUCh. 7.2 - Prob. 67AYUCh. 7.2 - Prob. 68AYUCh. 7.2 - Prob. 69AYUCh. 7.2 - Prob. 70AYUCh. 7.2 - Prob. 71AYUCh. 7.2 - Prob. 72AYUCh. 7.3 - Write the formula for the distance d from to ....Ch. 7.3 - Prob. 2AYUCh. 7.3 - Prob. 3AYUCh. 7.3 - Prob. 4AYUCh. 7.3 - Prob. 5AYUCh. 7.3 - Prob. 6AYUCh. 7.3 - Prob. 7AYUCh. 7.3 - Prob. 8AYUCh. 7.3 - In Problems 9-16, solve each triangle.Ch. 7.3 - In Problems 9-16, solve each triangle.Ch. 7.3 - In Problems 9-16, solve each triangle. Ch. 7.3 - Prob. 12AYUCh. 7.3 - Prob. 13AYUCh. 7.3 - Prob. 14AYUCh. 7.3 - Prob. 15AYUCh. 7.3 - Prob. 16AYUCh. 7.3 - Prob. 17AYUCh. 7.3 - Prob. 18AYUCh. 7.3 - Prob. 19AYUCh. 7.3 - Prob. 20AYUCh. 7.3 - Prob. 21AYUCh. 7.3 - Prob. 22AYUCh. 7.3 - Prob. 23AYUCh. 7.3 - Prob. 24AYUCh. 7.3 - Prob. 25AYUCh. 7.3 - Prob. 26AYUCh. 7.3 - Prob. 27AYUCh. 7.3 - Prob. 28AYUCh. 7.3 - Prob. 29AYUCh. 7.3 - Prob. 30AYUCh. 7.3 - Prob. 31AYUCh. 7.3 - Prob. 32AYUCh. 7.3 - Prob. 33AYUCh. 7.3 - Prob. 34AYUCh. 7.3 - Prob. 35AYUCh. 7.3 - Prob. 36AYUCh. 7.3 - Prob. 37AYUCh. 7.3 - Prob. 38AYUCh. 7.3 - Prob. 39AYUCh. 7.3 - Prob. 40AYUCh. 7.3 - Prob. 43AYUCh. 7.3 - Navigation An airplane flies due north from Ft....Ch. 7.3 - Avoiding a Tropical Storm A cruise ship maintains...Ch. 7.3 - Revising a Flight Plan In attempting to fly from...Ch. 7.3 - Major League Baseball Field A major league...Ch. 7.3 - Little League Baseball Field According to Little...Ch. 7.3 - Prob. 49AYUCh. 7.3 - Prob. 50AYUCh. 7.3 - Prob. 51AYUCh. 7.3 - Prob. 52AYUCh. 7.3 - Soccer Angles A soccer goal is 8 yards wide....Ch. 7.3 - Prob. 55AYUCh. 7.3 - Prob. 56AYUCh. 7.3 - Building a Swing Set Clint is building a wooden...Ch. 7.3 - Prob. 58AYUCh. 7.3 - Geometry Show that the length d of a chord of a...Ch. 7.3 - Prob. 60AYUCh. 7.3 - Prob. 61AYUCh. 7.3 - Prob. 62AYUCh. 7.3 - Prob. 63AYUCh. 7.3 - Prob. 64AYUCh. 7.3 - Prob. 65AYUCh. 7.3 - Prob. 66AYUCh. 7.3 - Prob. 67AYUCh. 7.3 - Prob. 68AYUCh. 7.3 - Prob. 69AYUCh. 7.3 - Prob. 70AYUCh. 7.3 - Prob. 71AYUCh. 7.4 - The area K of a triangle whose base is b and whose...Ch. 7.4 - Prob. 2AYUCh. 7.4 - Prob. 3AYUCh. 7.4 - Prob. 4AYUCh. 7.4 - Prob. 5AYUCh. 7.4 - Prob. 6AYUCh. 7.4 - Prob. 7AYUCh. 7.4 - Prob. 8AYUCh. 7.4 - Prob. 9AYUCh. 7.4 - Prob. 10AYUCh. 7.4 - Prob. 11AYUCh. 7.4 - Prob. 12AYUCh. 7.4 - Prob. 13AYUCh. 7.4 - Prob. 14AYUCh. 7.4 - Prob. 15AYUCh. 7.4 - Prob. 16AYUCh. 7.4 - Prob. 17AYUCh. 7.4 - Prob. 18AYUCh. 7.4 - Prob. 19AYUCh. 7.4 - Prob. 20AYUCh. 7.4 - Prob. 21AYUCh. 7.4 - Prob. 22AYUCh. 7.4 - Prob. 23AYUCh. 7.4 - Prob. 24AYUCh. 7.4 - Prob. 25AYUCh. 7.4 - Prob. 26AYUCh. 7.4 - Prob. 27AYUCh. 7.4 - Prob. 28AYUCh. 7.4 - Prob. 29AYUCh. 7.4 - Prob. 30AYUCh. 7.4 - Prob. 31AYUCh. 7.4 - Prob. 32AYUCh. 7.4 - Prob. 33AYUCh. 7.4 - Prob. 34AYUCh. 7.4 - Prob. 35AYUCh. 7.4 - Area of a Segment Find the area of the segment of...Ch. 7.4 - Prob. 37AYUCh. 7.4 - Prob. 38AYUCh. 7.4 - Prob. 39AYUCh. 7.4 - Prob. 40AYUCh. 7.4 - Prob. 41AYUCh. 7.4 - Prob. 42AYUCh. 7.4 - Prob. 43AYUCh. 7.4 - Bermuda Triangle The Bermuda Triangle is roughly...Ch. 7.4 - Prob. 45AYUCh. 7.4 - Prob. 46AYUCh. 7.4 - Perfect Triangles A perfect triangle is one having...Ch. 7.4 - Prob. 52AYUCh. 7.4 - Prob. 53AYUCh. 7.4 - Refer to Problem 109 in section 6.5. Show that the...Ch. 7.4 - Prob. 55AYUCh. 7.4 - Prob. 56AYUCh. 7.4 - Prob. 57AYUCh. 7.4 - Prob. 58AYUCh. 7.4 - Prob. 59AYUCh. 7.4 - Prob. 60AYUCh. 7.4 - Prob. 61AYUCh. 7.4 - Prob. 62AYUCh. 7.4 - Prob. 63AYUCh. 7.4 - Prob. 64AYUCh. 7.4 - Prob. 65AYUCh. 7.4 - Prob. 66AYUCh. 7.5 - The amplitude A and period T of f( x )=5sin( 4x )...Ch. 7.5 - Prob. 2AYUCh. 7.5 - Prob. 3AYUCh. 7.5 - Prob. 4AYUCh. 7.5 - In Problems 5-8, an object attached to a coiled...Ch. 7.5 - Prob. 6AYUCh. 7.5 - Prob. 7AYUCh. 7.5 - Prob. 8AYUCh. 7.5 - Rework Problem 7 under the same conditions, except...Ch. 7.5 - Rework Problem 8 under the same conditions, except...Ch. 7.5 - Rework Problem 9 under the same conditions, except...Ch. 7.5 - Rework Problem 10 under the same conditions,...Ch. 7.5 - Prob. 13AYUCh. 7.5 - Prob. 14AYUCh. 7.5 - Prob. 15AYUCh. 7.5 - Prob. 16AYUCh. 7.5 - Prob. 17AYUCh. 7.5 - Prob. 18AYUCh. 7.5 - Prob. 19AYUCh. 7.5 - Prob. 20AYUCh. 7.5 - Prob. 21AYUCh. 7.5 - Prob. 22AYUCh. 7.5 - Prob. 23AYUCh. 7.5 - Prob. 24AYUCh. 7.5 - Prob. 25AYUCh. 7.5 - Prob. 26AYUCh. 7.5 - Prob. 27AYUCh. 7.5 - Prob. 28AYUCh. 7.5 - Prob. 29AYUCh. 7.5 - Prob. 30AYUCh. 7.5 - Prob. 31AYUCh. 7.5 - Prob. 32AYUCh. 7.5 - Prob. 33AYUCh. 7.5 - Prob. 34AYUCh. 7.5 - Prob. 35AYUCh. 7.5 - Prob. 36AYUCh. 7.5 - Prob. 37AYUCh. 7.5 - Prob. 38AYUCh. 7.5 - Prob. 39AYUCh. 7.5 - Prob. 40AYUCh. 7.5 - Prob. 41AYUCh. 7.5 - Prob. 42AYUCh. 7.5 - Prob. 43AYUCh. 7.5 - Prob. 44AYUCh. 7.5 - Prob. 45AYUCh. 7.5 - Prob. 46AYUCh. 7.5 - Prob. 47AYUCh. 7.5 - Prob. 48AYUCh. 7.5 - Prob. 49AYUCh. 7.5 - Prob. 50AYUCh. 7.5 - Prob. 51AYUCh. 7.5 - Prob. 52AYUCh. 7.5 - Prob. 53AYUCh. 7.5 - Prob. 54AYUCh. 7.5 - Prob. 55AYUCh. 7.5 - Prob. 56AYUCh. 7.5 - Touch- Tone Phone On a Touch Tone Phone, each...Ch. 7.5 - Prob. 58AYUCh. 7.5 - Use a graphing utility to graph the function , ....Ch. 7.5 - Prob. 62AYUCh. 7.5 - Prob. 63AYUCh. 7.5 - Prob. 64AYUCh. 7.5 - Prob. 65AYUCh. 7.5 - Prob. 66AYUCh. 7.5 - Prob. 67AYUCh. 7.5 - If cos=45,02, find the exact value of: cos2 sin2...Ch. 7 - In Problems 1 and 2, find the exact value of the...Ch. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - In Problems 8-20, find the remaining angle(s) and...Ch. 7 - In Problems 8-20, find the remaining angle(s) and...Ch. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Constructing a Highway A highway whose primary...Ch. 7 - Approximating the Area of a Lake To approximate...Ch. 7 - Finding the Bearing of a Ship The Majesty leaves...Ch. 7 - Drive Wheels of an Engine The drive wheel of an...Ch. 7 - Prob. 38RECh. 7 - Simple Harmonic Motion An object attached to a...Ch. 7 - 43. The displacement d (in meter) of the bob of a...Ch. 7 - Find the exact value of the six trigonometric...Ch. 7 - Find the exact value of sin40cos50.Ch. 7 - In Problem 35, use the given information to...Ch. 7 - In Problem 35, use the given information to...Ch. 7 - In Problem 35, use the given information to...Ch. 7 - In Problem 68, solve each triangle. A=55, C=20,...Ch. 7 - In Problem 68, solve each triangle. a=3, b=7, A=40Ch. 7 - In Problem 68, solve each triangle. a=8, b=4, C=70Ch. 7 - Prob. 9CTCh. 7 - Prob. 10CTCh. 7 - Prob. 11CTCh. 7 - A hot- air balloon is flying at a height of 600...Ch. 7 - Prob. 13CTCh. 7 - Prob. 14CTCh. 7 - Madison wants to swim across Lake William from the...Ch. 7 - Prob. 16CTCh. 7 - Prob. 17CTCh. 7 - Prob. 18CTCh. 7 - Prob. 1CRCh. 7 - Prob. 2CRCh. 7 - Prob. 3CRCh. 7 - Prob. 4CRCh. 7 - Prob. 5CRCh. 7 - Prob. 6CRCh. 7 - Prob. 7CRCh. 7 - Prob. 8CRCh. 7 - Prob. 9CRCh. 7 - Prob. 10CRCh. 7 - Prob. 11CRCh. 7 - Prob. 12CRCh. 7 - Prob. 13CRCh. 7 - Prob. 14CR
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