Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

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

Answer

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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