# Chapter 8 - Right Triangles and Trigonometry - 8-1 The Pythagorean Theorem and It's Converse - Practice and Problem-Solving Exercises - Page 496: 32

acute

#### 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 4. Substitute the other two values, $\sqrt 11$ and $\sqrt 7$, in for a and b. $c^{2}$$\square$$a^{2}$+$b^{2}$ $4^{2}$$\square$$(\sqrt 11)^{2}$+$(\sqrt 7)^{2}$ 16$\square$11+7 16$\square$18 16$\lt$18 Since $c^{2}$$\lt$$a^{2}$+$b^{2}$, the triangle is acute

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