College Algebra & Trigonometry - Standalone book
College Algebra & Trigonometry - Standalone book
1st Edition
ISBN: 9780078035623
Author: Julie Miller, Donna Gerken
Publisher: McGraw-Hill Education
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Concept explainers

Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
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Chapter 7.1, Problem 28PE

A large weather balloon is tethered by two ropes. One rope measures 23 ft and attaches to the balloon at an angle of 32° from the ground. The second rope attaches to the base of the balloon at an angle of 150 with the ground.
a. How far from the ground is the balloon floating? Round to the nearest tenth of a foot.
b. Find the length of the second rope. Round to the nearest tenth of a foot.
c. If both ropes suddenly detach and the balloon rises straight tip at a rate of 3 ft/sec, how long will it take the balloon to reach a height of 50 ft from the ground? Round to the nearest tenth of a second.

Chapter 7.1, Problem 28PE, A large weather balloon is tethered by two ropes. One rope measures 23 ft and attaches to the

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Chapter 7 Solutions

College Algebra & Trigonometry - Standalone book

Ch. 7.1 - In a right triangle, one leg measures 15 ft and...Ch. 7.1 - Prob. R.2PECh. 7.1 - Prob. 1PECh. 7.1 - For Exercises 1-2, refer to triangle ABC. 2. The...Ch. 7.1 - Prob. 3PECh. 7.1 - Prob. 4PECh. 7.1 - For Exercises 5-12, given right triangle ABC,...Ch. 7.1 - Prob. 6PECh. 7.1 - For Exercises 5-12, given right triangle ABC,...Ch. 7.1 - Prob. 8PE
Ch. 7.1 - Prob. 9PECh. 7.1 - Prob. 10PECh. 7.1 - Prob. 11PECh. 7.1 - Prob. 12PECh. 7.1 - Note: Due to round-off error, the answers to...Ch. 7.1 - Prob. 14PECh. 7.1 - Note: Due to round-off error, the answers to...Ch. 7.1 - Prob. 16PECh. 7.1 - Note: Due to round-off error, the answers to...Ch. 7.1 - Prob. 18PECh. 7.1 - A boat is anchored off Elliot Key, Florida. From...Ch. 7.1 - A swimming pool has a depth of 4 ft at the shallow...Ch. 7.1 - An airplane climbs at an angle of 11° at an...Ch. 7.1 - Prob. 22PECh. 7.1 - A railroad bridge over New Scotland Road in...Ch. 7.1 - At 11:30A.M. the angle of elevation of the sun for...Ch. 7.1 - Prob. 25PECh. 7.1 - Prob. 26PECh. 7.1 - A police officer hiding between two bushes 50 ft...Ch. 7.1 - A large weather balloon is tethered by two ropes....Ch. 7.1 - Prob. 29PECh. 7.1 - Prob. 30PECh. 7.1 - To approximate the distance from the Earth to...Ch. 7.1 - Prob. 32PECh. 7.1 - A sewer line must have a minimum slope of 0.25 in....Ch. 7.1 - In order for gravel roads to have proper drainage,...Ch. 7.1 - The weather satellite NOAA- 15 orbits the Earth...Ch. 7.1 - Prob. 36PECh. 7.1 - a. Find the bearing from O to A. (See Example 5)...Ch. 7.1 - Prob. 38PECh. 7.1 - Prob. 39PECh. 7.1 - Prob. 40PECh. 7.1 - Prob. 41PECh. 7.1 - Prob. 42PECh. 7.1 - For Exercises 43-46, find the bearing of the ship....Ch. 7.1 - Prob. 44PECh. 7.1 - Prob. 45PECh. 7.1 - For Exercises 43-46, find the bearing of the ship....Ch. 7.1 - Prob. 47PECh. 7.1 - Prob. 48PECh. 7.1 - For Exercises 47-50, find the bearing to the...Ch. 7.1 - For Exercises 47-50, find the bearing to the...Ch. 7.1 - Prob. 51PECh. 7.1 - For Exercises 51-54, round answers to the nearest...Ch. 7.1 - Prob. 53PECh. 7.1 - Prob. 54PECh. 7.1 - Prob. 55PECh. 7.1 - Prob. 56PECh. 7.1 - A boat leaves a dock at a bearing of N42°W and...Ch. 7.1 - Prob. 58PECh. 7.1 - Prob. 59PECh. 7.1 - For Exercises 59-60, find the lengths of the sides...Ch. 7.1 - Prob. 61PECh. 7.1 - Prob. 62PECh. 7.1 - Prob. 63PECh. 7.1 - Prob. 64PECh. 7.1 - Prob. 65PECh. 7.1 - Prob. 66PECh. 7.1 - Prob. 67PECh. 7.1 - Prob. 68PECh. 7.1 - An airplane needs to fly to an airfield located...Ch. 7.1 - Prob. 70PECh. 7.1 - Prob. 71PECh. 7.1 - Prob. 72PECh. 7.1 - Prob. 73PECh. 7.1 - Prob. 74PECh. 7.1 - A contractor building eight ocean-front...Ch. 7.1 - Prob. 76PECh. 7.1 - Prob. 77PECh. 7.1 - Prob. 78PECh. 7.1 - Prob. 79PECh. 7.1 - Prob. 80PECh. 7.2 - Use a calculator to approximate the value of sin-1...Ch. 7.2 - Prob. R.2PECh. 7.2 - Prob. 1PECh. 7.2 - Prob. 2PECh. 7.2 - Prob. 3PECh. 7.2 - Prob. 4PECh. 7.2 - Prob. 5PECh. 7.2 - Prob. 6PECh. 7.2 - Note: Due to round-off error, the answers to...Ch. 7.2 - Note: Due to round-off error, the answers to...Ch. 7.2 - Note: Due to round-off error, the answers to...Ch. 7.2 - Note: Due to round-off error, the answers to...Ch. 7.2 - Note: Due to round-off error, the answers to...Ch. 7.2 - Prob. 12PECh. 7.2 - For Exercises 13-20, solve ABC subject to the...Ch. 7.2 - Prob. 14PECh. 7.2 - Prob. 15PECh. 7.2 - Prob. 16PECh. 7.2 - For Exercises 13-20, solve ABC subject to the...Ch. 7.2 - Prob. 18PECh. 7.2 - Prob. 19PECh. 7.2 - Prob. 20PECh. 7.2 - For Exercises 21-28, information is given about...Ch. 7.2 - For Exercises 21-28, information is given about...Ch. 7.2 - For Exercises 21-28, information is given about...Ch. 7.2 - For Exercises 21-28, information is given about...Ch. 7.2 - Prob. 25PECh. 7.2 - Prob. 26PECh. 7.2 - For Exercises 21-28, information is given about...Ch. 7.2 - For Exercises 21-28, information is given about...Ch. 7.2 - For Exercises 29-34, find the area of a triangle...Ch. 7.2 - Prob. 30PECh. 7.2 - Prob. 31PECh. 7.2 - Prob. 32PECh. 7.2 - For Exercises 29-34, find the area of a triangle...Ch. 7.2 - Prob. 34PECh. 7.2 - The area in the Atlantic Ocean known as the...Ch. 7.2 - The triangular face of a gabled roof measures 33.8...Ch. 7.2 - Prob. 37PECh. 7.2 - A helicopter is on a path directly overhead line...Ch. 7.2 - Prob. 39PECh. 7.2 - Prob. 40PECh. 7.2 - Prob. 41PECh. 7.2 - Prob. 42PECh. 7.2 - A wire is fastened to a point T on a tree and to...Ch. 7.2 - The Leaning Tower of Suurhusen is a medieval...Ch. 7.2 - A 25-ft flag pole is oriented vertically at the...Ch. 7.2 - Prob. 46PECh. 7.2 - Two residential buildings are to be constructed...Ch. 7.2 - A hiker wants to estimate the height of a mountain...Ch. 7.2 - A surveyor fixes a 420-ft baseline between points...Ch. 7.2 - Prob. 50PECh. 7.2 - The connector rod from the piston to the...Ch. 7.2 - Prob. 52PECh. 7.2 - For Exercises 53-66, solve ABC . Round the lengths...Ch. 7.2 - Prob. 54PECh. 7.2 - For Exercises 53-66, solve ABC . Round the lengths...Ch. 7.2 - Prob. 56PECh. 7.2 - For Exercises 53-66, solve ABC . Round the lengths...Ch. 7.2 - For Exercises 53-66, solve ABC . Round the lengths...Ch. 7.2 - For Exercises 53-66, solve ABC . Round the lengths...Ch. 7.2 - Prob. 60PECh. 7.2 - For Exercises 53-66, solve ABC . Round the lengths...Ch. 7.2 - Prob. 62PECh. 7.2 - For Exercises 53-66, solve ABC . Round the lengths...Ch. 7.2 - Prob. 64PECh. 7.2 - For Exercises 53-66, solve ABC . Round the lengths...Ch. 7.2 - Prob. 66PECh. 7.2 - After a hurricane, a homeowner examines trees on...Ch. 7.2 - Prob. 68PECh. 7.2 - Consider a sector of a circle of radius 6 cm with...Ch. 7.2 - Prob. 70PECh. 7.2 - Prob. 71PECh. 7.2 - Prob. 72PECh. 7.2 - Prob. 73PECh. 7.2 - Prob. 74PECh. 7.2 - Prob. 75PECh. 7.2 - Prob. 76PECh. 7.2 - Prob. 77PECh. 7.2 - Use the law of sines in the form sinAsinB=ab to...Ch. 7.2 - Use the relationships ac=sinAsinC and bc=sinBsinC...Ch. 7.2 - Prob. 80PECh. 7.3 - Find the exact distance between the points (-7, 2)...Ch. 7.3 - Prob. R.2PECh. 7.3 - Prob. R.3PECh. 7.3 - Prob. 1PECh. 7.3 - Prob. 2PECh. 7.3 - Prob. 3PECh. 7.3 - Prob. 4PECh. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - Prob. 7PECh. 7.3 - Prob. 8PECh. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - Prob. 16PECh. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - Prob. 18PECh. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - For Exercises 5-22, solve ABC subject to the given...Ch. 7.3 - A boat leaves port and follows a course of N77°E...Ch. 7.3 - Prob. 24PECh. 7.3 - Two planes leave the same airport. The first plane...Ch. 7.3 - Two boats leave a marina at tile same time. The...Ch. 7.3 - A 40-ft boom on a crane is attached to the crane...Ch. 7.3 - Prob. 28PECh. 7.3 - A regulation fast-pitch softball diamond for high...Ch. 7.3 - The Flatiron Building in New York City is said to...Ch. 7.3 - The distance between Dallas, Texas, and Atlanta,...Ch. 7.3 - Prob. 32PECh. 7.3 - A 150-ft tower is anchored on a hill by two guy...Ch. 7.3 - Prob. 34PECh. 7.3 - In Exercises 35-38, use Heron’s formula to find...Ch. 7.3 - In Exercises 35-38, use Heron’s formula to find...Ch. 7.3 - Prob. 37PECh. 7.3 - Prob. 38PECh. 7.3 - Prob. 39PECh. 7.3 - Prob. 40PECh. 7.3 - Prob. 41PECh. 7.3 - Prob. 42PECh. 7.3 - Prob. 43PECh. 7.3 - Prob. 44PECh. 7.3 - Prob. 45PECh. 7.3 - Prob. 46PECh. 7.3 - Three mutually tangential circles with radii...Ch. 7.3 - Prob. 48PECh. 7.3 - Prob. 49PECh. 7.3 - Prob. 50PECh. 7.3 - Prob. 51PECh. 7.3 - Prob. 52PECh. 7.3 - Prob. 53PECh. 7.3 - Prob. 54PECh. 7.3 - Prob. 55PECh. 7.3 - Prob. 56PECh. 7.3 - Prob. 57PECh. 7.3 - Prob. 58PECh. 7.3 - Prob. 59PECh. 7.3 - Prob. 60PECh. 7.4 - Identify the amplitude and period. y = 2cos 4xCh. 7.4 - Prob. R.2PECh. 7.4 - Prob. R.3PECh. 7.4 - Prob. 1PECh. 7.4 - Prob. 2PECh. 7.4 - Prob. 3PECh. 7.4 - Prob. 4PECh. 7.4 - The frequency of middle C on a piano is 264 Hz....Ch. 7.4 - Prob. 6PECh. 7.4 - For Exercises 7-14, suppose that an object moves...Ch. 7.4 - Prob. 8PECh. 7.4 - For Exercises 7-14, suppose that an object moves...Ch. 7.4 - For Exercises 7-14, suppose that an object moves...Ch. 7.4 - For Exercises 7-14, suppose that an object moves...Ch. 7.4 - Prob. 12PECh. 7.4 - Prob. 13PECh. 7.4 - Prob. 14PECh. 7.4 - Prob. 15PECh. 7.4 - Prob. 16PECh. 7.4 - Prob. 17PECh. 7.4 - Prob. 18PECh. 7.4 - Prob. 19PECh. 7.4 - Prob. 20PECh. 7.4 - Prob. 21PECh. 7.4 - Prob. 22PECh. 7.4 - A block hangs 01) a spring attached to the ceiling...Ch. 7.4 - The bob on a simple pendulum is pulled to the left...Ch. 7.4 - A 7-in, connecting rod in an engine connects the...Ch. 7.4 - Prob. 26PECh. 7.4 - A Ferris wheel at a county Fair is 180 ft in...Ch. 7.4 - The 30-fl diameter waterwheel at Deleon Springs...Ch. 7.4 - Prob. 29PECh. 7.4 - Prob. 30PECh. 7.4 - Prob. 31PECh. 7.4 - Prob. 32PECh. 7.4 - The angular displacement 6 (in radians) of a...Ch. 7.4 - The angular displacement 6 (in radians) of a...Ch. 7.4 - The brightness of a “young” star sometimes...Ch. 7.4 - Prob. 36PECh. 7.4 - For Exercises 37-38, the ordered pair (t, d) gives...Ch. 7.4 - Prob. 38PECh. 7.4 - Write a function y=f(t) for simple harmonic motion...Ch. 7.4 - Write a function y=f(t) for simple harmonic motion...Ch. 7.4 - Use a graphing utility to graph the functions of...Ch. 7.4 - Show that the graph of d=aectcost is bounded by...Ch. 7.4 - Prob. 43PECh. 7.4 - Prob. 44PECh. 7.4 - Prob. 45PECh. 7.4 - Prob. 46PECh. 7.4 - Prob. 47PECh. 7.4 - Prob. 48PECh. 7.4 - Prob. 49PECh. 7.4 - Prob. 50PECh. 7.4 - Prob. 51PECh. 7.4 - Prob. 52PECh. 7.4 - Prob. 53PECh. 7.4 - Prob. 54PECh. 7.4 - Prob. 55PECh. 7.4 - Prob. 56PECh. 7.4 - Given the model d=20e0.6tcos2t , for an object in...Ch. 7.4 - Prob. 58PECh. 7 - For Exercises 1-12, solve ABC subject to the given...Ch. 7 - Prob. 2PRECh. 7 - Prob. 3PRECh. 7 - Prob. 4PRECh. 7 - Prob. 5PRECh. 7 - Prob. 6PRECh. 7 - Prob. 7PRECh. 7 - Prob. 8PRECh. 7 - Prob. 9PRECh. 7 - Prob. 10PRECh. 7 - Prob. 11PRECh. 7 - Prob. 12PRECh. 7 - Prob. 13PRECh. 7 - Prob. 14PRECh. 7 - Prob. 15PRECh. 7 - Prob. 1RECh. 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 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - For Exercises 21-22, find the area of a triangle...Ch. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Points A, B. and P are collinear points along a...Ch. 7 - Prob. 28RECh. 7 - For Exercises 29-32, solve ABC subject to the...Ch. 7 - For Exercises 29-32, solve ABC subject to the...Ch. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - A boat leaves a marina and travels due south for 1...Ch. 7 - Prob. 40RECh. 7 - Two sides of a triangular plot of land measure 510...Ch. 7 - A gardener digs out a space for a triangular...Ch. 7 - For Exercises 43-46, suppose that an object moves...Ch. 7 - For Exercises 43-46, suppose that an object moves...Ch. 7 - For Exercises 43-46, suppose that an object moves...Ch. 7 - Prob. 46RECh. 7 - Prob. 47RECh. 7 - Prob. 48RECh. 7 - Prob. 49RECh. 7 - A Ferris wheel is 200 ft in diameter with its...Ch. 7 - Prob. 51RECh. 7 - Prob. 52RECh. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - Prob. 3TCh. 7 - Prob. 4TCh. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Prob. 9TCh. 7 - Prob. 10TCh. 7 - Prob. 11TCh. 7 - Prob. 12TCh. 7 - Prob. 13TCh. 7 - Prob. 14TCh. 7 - Prob. 15TCh. 7 - Prob. 16TCh. 7 - Prob. 17TCh. 7 - Prob. 18TCh. 7 - Prob. 19TCh. 7 - Prob. 20TCh. 7 - Prob. 21TCh. 7 - Prob. 22TCh. 7 - Prob. 23TCh. 7 - A block hangs on a spring attached to the ceiling...Ch. 7 - Prob. 25TCh. 7 - Prob. 26TCh. 7 - Prob. 27TCh. 7 - Prob. 1CRECh. 7 - Prob. 2CRECh. 7 - Prob. 3CRECh. 7 - Prob. 4CRECh. 7 - Prob. 5CRECh. 7 - Prob. 6CRECh. 7 - Prob. 7CRECh. 7 - Write an equation for a sine function with an...Ch. 7 - Write an equation for a tangent function with a...Ch. 7 - Prob. 10CRECh. 7 - Prob. 11CRECh. 7 - Prob. 12CRECh. 7 - Prob. 13CRECh. 7 - Prob. 14CRECh. 7 - Prob. 15CRECh. 7 - Prob. 16CRECh. 7 - Simplify to a single trigonometric function....Ch. 7 - Find the exact value of cos200cos50+sin200sin50Ch. 7 - Prob. 19CRECh. 7 - Prob. 20CRE
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Trigonometric Ratios; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9-eHMMpQC2k;License: Standard YouTube License, CC-BY