# Chapter 8 - Right Triangles and Trigonometry - 8-1 The Pythagorean Theorem and It's Converse - Practice and Problem-Solving Exercises - Page 496: 31

right

#### 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 50. Substitute the other two values, 30 and 40, in for a and b $c^{2}$$\square$$a^{2}$+$b^{2}$ $50^{2}$$\square$$30^{2}$+$40^{2}$ 2500$\square$900+1600 2500$\square$2500 2500$=$2500 Since $c^{2}$$=$$a^{2}$+$b^{2}$, the triangle is right.

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