## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 8 - Right Triangles and Trigonometry - 8-1 The Pythagorean Theorem and It's Converse - Practice and Problem-Solving Exercises - Page 496: 30

obtuse

#### Work Step by Step

Comparing the square of the longest side to the sum of the squares of the other two sides will tell you if a triangle is obtuse, acute, or right. If $c^{2}$$\gt$$a^{2}$+$b^{2}$, then the triangle is obtuse If $c^{2}$$\lt$$a^{2}$+$b^{2}$, then the triangle is acute If $c^{2}$$=$$a^{2}$+$b^{2}$, then the triangle is right Substitute in the greatest value in for c, which is 3. Substitute the other two values, 2 and $\sqrt 3$, in for a and b. $c^{2}$$\square$$a^{2}$+$b^{2}$ $3^{2}$$\square$$2^{2}$+$(\sqrt 3)^{2}$ 9$\square$4+3 9$\square$7 9$\gt$7 Since $c^{2}$$\gt$$a^{2}$+$b^{2}$, the triangle is obtuse

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