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7th Edition

James Stewart + 2 others

Publisher: Brooks Cole

ISBN: 9781305071759

Chapter 6.1, Problem 82E

Textbook Problem

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**Irrigation** An irrigation system uses a straight sprinkler pipe 300 ft long that pivots around a central point as shown. Because of an obstacle the pipe is allowed to pivot through 280° only. Find the area irrigated by this system.

To determine

**To find:** The area of the irrigated part from the sprinkler pipe.

**Given:**

Length of the sprinkler pipe is

Angle is

**Formulas used:**

Area of the circular sector is,

Here

Area of a circle is,

Conversion of degree to radian

**Calculation:**

The sprinkler pipe makes a circular path covering the irrigated portion.

Therefore the area is taken as a circle of angle

Angle for the sector is,

Convert degree to radian.

Formula for area of a circular sector is,

Substitute

Area of the circular sector is

Formula for area of circle,

Substitute

The area of circle is

Precalculus: Mathematics for Calculus (Standalone Book)

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Find the indicated...Ch. 6.6 - Herons Formula Find the area of the triangle whose...Ch. 6.6 - Herons Formula Find the area of the triangle whose...Ch. 6.6 - Herons Formula Find the area of the triangle whose...Ch. 6.6 - Herons Formula Find the area of the triangle whose...Ch. 6.6 - Herons Formula Find the area of the shaded figure,...Ch. 6.6 - Herons Formula Find the area of the shaded figure,...Ch. 6.6 - Herons Formula Find the area of the shaded figure,...Ch. 6.6 - Herons Formula Find the area of the shaded figure,...Ch. 6.6 - Area of a Region Three circles of radii 4, 5, and...Ch. 6.6 - Finding a Length In the figure, triangle ABC is a...Ch. 6.6 - Surveying To find the distance across a small...Ch. 6.6 - Geometry A parallelogram has sides of lengths 3...Ch. 6.6 - Calculating Distance Two straight roads diverge at...Ch. 6.6 - Calculating Distance A car travels along a...Ch. 6.6 - Dead Reckoning A pilot flies in a straight path...Ch. 6.6 - Navigation Two boats leave the same port at the...Ch. 6.6 - Navigation A fisherman leaves his home port and...Ch. 6.6 - Navigation Airport B is 300 mi from airport A at a...Ch. 6.6 - Triangular Field A triangular field has sides of...Ch. 6.6 - Towing a Barge Two tugboats that are 120 ft apart...Ch. 6.6 - Flying Kites A boy is flying two kites at the same...Ch. 6.6 - Securing a Tower A 125-ft tower is located on the...Ch. 6.6 - Cable Car A steep mountain is inclined 74 to the...Ch. 6.6 - CN Tower The CN Tower in Toronto, Canada, is the...Ch. 6.6 - Land Value Land in downtown Columbia is valued at...Ch. 6.6 - DISCUSS: Solving for the Angles in a Triangle The...Ch. 6.6 - PROVE: Projection Laws Prove that in triangle ABC...Ch. 6 - (a) How is the degree measure of an angle defined?...Ch. 6 - (a) When is an angle in standard position?...Ch. 6 - (a) In a circle of radius r, what is the length s...Ch. 6 - (a) Let be an acute angle in a right triangle....Ch. 6 - (a) What does it mean to solve a triangle? (b)...Ch. 6 - (a) Let be an angle in standard position, let...Ch. 6 - In each of the four quadrants, identify the...Ch. 6 - (a) Describe the steps we use to find the value of...Ch. 6 - (a) State the reciprocal identities. (b) State the...Ch. 6 - (a) What is the area of a triangle with sides of...Ch. 6 - (a) Define the inverse sine function, the inverse...Ch. 6 - (a) State the Law of Sines. (b) Find side a in the...Ch. 6 - (a) State the Law of Cosines. (b) Find side a in...Ch. 6 - From Degrees to Radians Find the radian measure...Ch. 6 - From Degrees to Radians Find the radian measure...Ch. 6 - From Radians to Degrees Find the degree measure...Ch. 6 - From Radians to Degrees Find the degree measure...Ch. 6 - Length of a Circular Arc These exercises involve...Ch. 6 - A central angle in a circle of radius 2.5 cm is...Ch. 6 - A circular arc of length 25 ft subtends a central...Ch. 6 - A circular arc of length 13 m subtends a central...Ch. 6 - Length of a Circular Arc These exercises involve...Ch. 6 - New York and Los Angeles are 2450 mi apart. Find...Ch. 6 - Area of a Circular Sector These exercises involve...Ch. 6 - Area of a Circular Sector These exercises involve...Ch. 6 - Area of a Circular Sector These exercises involve...Ch. 6 - Area of a Circular Sector These exercises involve...Ch. 6 - Angular Speed and Linear Speed A potters wheel...Ch. 6 - Angular Speed and Linear Speed In an automobile...Ch. 6 - Trigonometric Ratios Find the values of the six...Ch. 6 - Trigonometric Ratios Find the values of the six...Ch. 6 - Finding Sides in Right Triangles Find the sides...Ch. 6 - Finding Sides in Right Triangles Find the sides...Ch. 6 - Finding Sides in Right Triangles Find the sides...Ch. 6 - Finding Sides in Right Triangles Find the sides...Ch. 6 - Solving a Triangle Solve the triangle. 23.Ch. 6 - Solving a Triangle Solve the triangle. 24.Ch. 6 - Solving a Triangle Solve the triangle. 25.Ch. 6 - Solving a Triangle Solve the triangle. 26.Ch. 6 - Trigonometric Ratios Express the lengths a and b...Ch. 6 - CN Tower The highest free-standing tower in North...Ch. 6 - Perimeter of a Regular Hexagon Find the perimeter...Ch. 6 - Pistons of an Engine The pistons in a car engine...Ch. 6 - Radius of the Moon As viewed from the earth, the...Ch. 6 - Distance Between Two Ships A pilot measures the...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the exact...Ch. 6 - Values of Trigonometric Functions Find the values...Ch. 6 - Values of Trigonometric Functions Find sin if is...Ch. 6 - Angle Formed by a Line Find the acute angle that...Ch. 6 - Values of Trigonometric Functions Find the six...Ch. 6 - Expressing One Trigonometric Function in Terms of...Ch. 6 - Expressing One Trigonometric Function in Terms of...Ch. 6 - Expressing One Trigonometric Function in Terms of...Ch. 6 - Expressing One Trigonometric Function in Terms of...Ch. 6 - Values of Trigonometric Functions Find the values...Ch. 6 - Values of Trigonometric Functions Find the values...Ch. 6 - Values of Trigonometric Functions Find the values...Ch. 6 - Values of Trigonometric Functions Find the values...Ch. 6 - Value of an Expression Find the value of the given...Ch. 6 - Value of an Expression Find the value of the given...Ch. 6 - Value of an Expression Find the value of the given...Ch. 6 - Value of an Expression Find the value of the given...Ch. 6 - Values of Inverse Trigonometric Functions Find the...Ch. 6 - Values of Inverse Trigonometric Functions Find the...Ch. 6 - Values of Inverse Trigonometric Functions Find the...Ch. 6 - Values of Inverse Trigonometric Functions Find the...Ch. 6 - Inverse Trigonometric Functions Rewrite the...Ch. 6 - Inverse Trigonometric Functions Rewrite the...Ch. 6 - Finding an Unknown Side Express in terms of x....Ch. 6 - Finding an Unknown Side Express in terms of x....Ch. 6 - Law of Sines and Law of Cosines Find the side...Ch. 6 - Law of Sines and Law of Cosines Find the side...Ch. 6 - Law of Sines and Law of Cosines Find the side...Ch. 6 - Law of Sines and Law of Cosines Find the side...Ch. 6 - Law of Sines and Law of Cosines Find the side...Ch. 6 - Law of Sines and Law of Cosines Find the side...Ch. 6 - Law of Sines and Law of Cosines Find the side...Ch. 6 - Law of Sines and Law of Cosines Find the side...Ch. 6 - Law of Sines and Law of Cosines Find the side...Ch. 6 - Law of Sines and Law of Cosines Find the side...Ch. 6 - Distance Between Two Ships Two ships leave a port...Ch. 6 - Height of a Building From a point A on the ground,...Ch. 6 - Distance Between Two Points Find the distance...Ch. 6 - Distance Between a Boat and the Shore A boat is...Ch. 6 - Area of a Triangle Find the area of a triangle...Ch. 6 - Herons Formula Find the area of a triangle with...Ch. 6 - Find the radian measures that correspond to the...Ch. 6 - Find the degree measures that correspond to the...Ch. 6 - The rotor blades of a helicopter are 16 ft long...Ch. 6 - Find the exact value of each of the following. (a)...Ch. 6 - Find tan + sin for the angle shown.Ch. 6 - Express the lengths a and b shown in the figure in...Ch. 6 - If cos=13 and is in Quadrant III, find tan cot ...Ch. 6 - If ssin=513 and tan=512, find sec .Ch. 6 - Express tan in terms of sec for in Quadrant II.Ch. 6 - The base of the ladder in the figure is 6 ft from...Ch. 6 - Express in each figure in terms of x. (a) (b)Ch. 6 - Find the exact value of cos(tan1910).Ch. 6 - Find the side labeled x or the angle labeled . 13.Ch. 6 - Find the side labeled x or the angle labeled . 14.Ch. 6 - Find the side labeled x or the angle labeled . 15.Ch. 6 - Find the side labeled x or the angle labeled . 16.Ch. 6 - Find the side labeled x or the angle labeled . 17.Ch. 6 - Find the side labeled x or the angle labeled . 18.Ch. 6 - Refer to the figure below. (a) Find the area of...Ch. 6 - Refer to the figure below. (a) Find the angle...Ch. 6 - Two wires tether a balloon to the ground, as...Ch. 6 - Completing the Map Find the distance between the...Ch. 6 - Completing the Map Find the distance between the...Ch. 6 - Determining a Distance A surveyor on one side of a...Ch. 6 - Height of a Cliff To measure the height of an...Ch. 6 - Height of a Mountain To calculate the height h of...Ch. 6 - Determining a Distance A surveyor has determined...Ch. 6 - Surveying Building Lots A surveyor surveys two...Ch. 6 - Great Survey of India The Great Trigonometric...

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