Explanation Approach: The following theorem is used to solve the problem: Pythagorean Theorem states that for a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Or, c 2 = a 2 + b 2 . The illustration is given below: The following steps have been followed to find out the answer: Step-1: Analyse the given problem and the image, and then redraw the image with naming to all points in the image. Step-2: Apply the values in the Pythagorean formula and find out the value of the first hypotenuse. Redraw the image with the known value. Step-3: Repeat the step-2 until to find out the length of the line segment A B in the given figure. Finally, write the answer. Calculation: The given figure is . From the figure, we can understand that all the triangles in the image are right triangles or right-angled triangles. To easily identify the points, we have to name them. We can redraw the image by naming the points as given below: If we want to find out the length of the line segment A B , we have to first find out the length of the line segment B D and then find out the length of the line segment B E . In the first triangle B C D , the length of the side B C = 1 and the length of the side C D = 1 We have to find out the length of the hypotenuse B D = ? 2) Since the triangle B C D is a right triangle, we can use the Pythagorean Theorem to find out the length of the hypotenuse. The Pythagorean Theorem states that for a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. The Pythagorean formula is c 2 = a 2 + b 2 or a 2 + b 2 = c 2 . Here, consider the side B C = a = 1 , C D = b = 1 and B D = c = ? . Apply these values to The Pythagorean formula. So, we get, c 2 = 1 2 + 1 2 . Apply the square rule to the left-hand side of the above equation and do the necessary simplification. So, we get, c 2 = 1 ⋅ 1 + 1 ⋅ 1 c 2 = 1 + 1 c 2 = 2 Take the square root to both sides of the equation then, c 2 = 2 c ⋅ c = 2 c = 2 Therefore, the length of the hypotenuse c = B D = 2 . Now, we can redraw the images as given below: 3) In the triangle B D E , the length of the side B D = 2 and the length of the side D E = 1 We have to find out the length of the hypotenuse B E = ? Since the triangle B D E is a right triangle, we can use the Pythagorean formula to find out the length of the hypotenuse. The Pythagorean formula is c 2 = a 2 + b 2 or a 2 + b 2 = c 2

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

See similar textbooks

Question

Chapter 6.4, Problem 91E

To determine

To find:

The length of the line segment AB in the given figure.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 90E

Chapter 6.4, Problem 92E

Students have asked these similar questions

Refer to page 90 for a problem involving the Laplace Transform of a given piecewise function. Solve it using properties of Laplace Transforms and inverse transforms. Provide a step-by-step solution with clear calculations. Instructions: Do not provide irrelevant content. Focus on solving the problem step-by-step and showing all calculations explicitly for clarity. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]

On page 83, a power series is given. Use the ratio test or root test to determine the radius of convergence. Show each calculation clearly, including intermediate steps and final conclusions. Instructions: Stick to the question. Provide step-by-step calculations for the radius of convergence and avoid irrelevant content. Ensure the solution is clear and detailed. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]

On page 95, a proof of the orthogonality of Legendre polynomials is discussed. Reconstruct the proof with detailed steps, using the weighted integral formulation for Legendre polynomials. Instructions: Stick to solving the problem only. Provide a clear outline, detailed steps, and all necessary calculations. Do not add irrelevant content. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]