---### Problem 20: Identifying a Right Triangle**Question:**Suppose a triangle has sides of length $ a $, $ b $, and $ c $ satisfying the equation \[ a^2 + b^2 = c^2. \]Show that this triangle is a right triangle.**Solution:**To determine if the given triangle is a right triangle, we will use the Pythagorean theorem. According to the Pythagorean theorem, a triangle with sides $ a $, $ b $, and $ c $ (where $ c $ is the hypotenuse) is a right triangle if and only if \[ a^2 + b^2 = c^2. \]In this problem, we are given that the sides $ a $, $ b $, and $ c $ satisfy this exact equation. Thus, by the Pythagorean theorem, the given triangle must be a right triangle.Conclusion: The given triangle is a right triangle because its sides satisfy the Pythagorean equation.---This concludes that whenever the equation $ a^2 + b^2 = c^2 $ holds true for the sides of a triangle, the triangle in question is definitively a right triangle.

We can prove this by contradiction- Let us assume a ∆ABC, that is not a right angled triangle but…

Answered: 20. Suppose a triangle has sides of…

20. Suppose a triangle has sides of length a, b, and c satisfying the equation a? + b? = c?. Show that this triangle is a right triangle.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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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