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Concept explainers
To find: To express the Area within the circle, but outside the triangle, as a function of the length of side of an equilateral triangle, inscribed inside the circle.
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Answer to Problem 17AYU
Solution:
Explanation of Solution
Given:
An equilateral triangle of side ‘’ is inscribed inside a circle of radius ‘’ as given below.
Calculation:
To express the Area within the circle, but outside the triangle, as a function of the length of side of an equilateral triangle, inscribed inside the circle.
Area of a circle of radius .
Area of an equilateral triangle of side .
Area that is within the circle but outside the triangle .
To represent radius interms of .
When an equilateral triangle is inscribed inside a circle, then the centre of the circle matches with the centroid of the triangle.
If side of the triangle then, height of the equilateral triangle .
Now, centroid of a triangle divides the height in the ratio 2:1.
Therefore, the distance between centroid to any vertices of the equilateral triangle of height of the equilateral triangle.
The area of the circle is .
Area that is within the circle but outside the triangle .
Therefore, .
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Glencoe Math Accelerated, Student Edition
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus (10th Edition)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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