Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 8 - Right Triangles and Trigonometry - Chapter Test - Page 537: 7

Answer

obtuse triangle

Work Step by Step

In an acute triangle, the square of the length of the longest side is shorter than the squares of the lengths of the other two sides; therefore, $c^2 < a^2 + b^2$ or $a^2 + b^2 > c^2$. In an obtuse triangle, the square of the length of the longest side is longer than the squares of the lengths of the other two sides; therefore, $c^2 > a^2 + b^2$, or $a^2 + b^2 < c^2$. Finally, in a right triangle, the square of the length of the longest side is equal to the squares of the lengths of the other two sides; therefore, $c^2 = a^2 + b^2$, or $a^2 + b^2 = c^2$. Let's find out what situation exists for the triangle with the given sides: $5^2 + 6^2$ ? $10^2$ Evaluate the exponents: $25 + 36$ ? $100$ Add to simplify: $61 < 100$ So $a^2 + b^2 < c^2$; therefore, this triangle is an obtuse triangle.
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