## 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: 28

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 0.6. Substitute the other two values 0.3 and 0.4 in for a and b $c^{2}$$\square$$a^{2}$+$b^{2}$ $0.6^{2}$$\square$$0.3^{2}$+$0.4^{2}$ 0.36$\square$0.09+0.16 0.36$\square$0.25 0.36$\gt$0.25 Since $c^{2}$$\gt$$a^{2}$+$b^{2}$, the triangle is obtuse

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