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CBSE Class 11-science Answered

in a right angled triangle the hypotenuse is 2root2 times the perpendicular drawn from  the opposite vertex then then other acute angles of triangle are   
Asked by gargpuneet989 | 10 Jul, 2018, 06:28: PM
answered-by-expert Expert Answer
begin mathsize 16px style Let space the space length space of space AB space equals space straight a space unit space and space BC space equals space straight b space unit. area space of space the space triangle space equals space 1 half ab space square space unit Hypotenuse space equals space 2 square root of 2 straight x Area space of space triangle space ABC space equals 1 half straight x cross times 2 square root of 2 straight x equals square root of 2 straight x squared space Area space of space both space triangles space are space same 1 half ab equals square root of 2 straight x squared space ab equals 2 square root of 2 straight x squared space using space Pythagoras space in space right space ngle space triangle space ABC comma AC to the power of 2 space end exponent equals AB squared plus BC squared open parentheses 2 square root of 2 straight x close parentheses squared equals straight a squared plus straight b squared........ left parenthesis straight i right parenthesis and space solving space we space get space straight b equals fraction numerator 2 square root of 2 straight x squared over denominator straight a end fraction Putting space the space value space of space straight b space in space left parenthesis straight i right parenthesis we space get space straight b equals square root of 4 straight x squared minus 2 square root of 2 straight x squared end root In space increment ABC comma tanC equals straight a over straight b equals square root of fraction numerator 2 plus square root of 2 over denominator 2 minus square root of 2 end fraction end root straight C equals 22.5 degree angle ACB equals straight pi over 8 Second space value space equals space 90 minus 22.5 degree equals 67.5 degree equals fraction numerator 3 straight pi over denominator 8 end fraction end style
Answered by Sneha shidid | 11 Jul, 2018, 11:23: AM

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