Explanation Given: In a right-angle triangle with sided 5,12 and 13ft, an ant starts at the vertex of the right angle and crawls straight towards the hypotenuse and its path is perpendicular to hypotenuse and creates two more right triangles. Then, the ant crawls towards the hypotenuse of smaller of two new right triangles and this creates two new right triangles and the ant crawls forever to create new right triangles. Formula used: The sum of geometric progression is S = a 1 − r , where a is the first terms and r is the common ratio of the series. Calculation: The ant is traveling from vertex to the point in hypotenuse as shown in figure. It is clear from the figure that angle θ remains constant for both the right-angle triangles that is for large as well as small. This implies, sin θ = 5 13 = x 12 Therefore, the distance that ant crawls for making two small triangles rom the big one is: x 12 = 5 13 x = 5 13 × 12 So, the distance is x = 12 r , where r = 5 13

6th Edition

ISBN: 9780321916600

Author: Mark Dugopolski

Publisher: PEARSON

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8.3, Problem 115E

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To calculate: The total distance traveled by an ant provided that in a right-angled triangle with sides 5,12 and 13ft. An ant starts at the vertex of the right angle and crawl straight towards the hypotenuse its path is perpendicular to hypotenuse and create two more right triangles then the ant crawls towards the hypotenuse of smaller of two new right triangles. This creates two new right triangles and the ant crawls forever to create new right triangles.

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Chapter 8.3, Problem 114E

Chapter 8.3, Problem 116E

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Solution Summary: The author calculates the total distance traveled by an ant in a right-angled triangle with sides 5,12 and 13ft.

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