## Trigonometry 7th Edition

Published by Cengage Learning

# Chapter 2 - Section 2.1 - Definition II: Right Triangle Trigonometry - 2.1 Problem Set: 74

x= -1 or 3

#### Work Step by Step

To calculate VALUE OF 'x' , we will use distance formula- r= $\sqrt { (x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2}}$ As per given data $\sqrt 13$ = $\sqrt { (1 - x) ^{2} + (5 -2) ^{2}}$ $\sqrt 13$ = $\sqrt { 1 - 2x +x^{2} + 9 }$ [ on expanding $(1 - x)^{2}$] $\sqrt 13$ = $\sqrt { x^{2} - 2x + 10 }$ Squaring both the sides- 13 = $x^{2} - 2x + 10$ Rearranging- $x^{2} - 2x -3$ = 0 Factorizing the L.H.S.- (x+1) (x-3) = 0 Therefore Either x = -1 or 3

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