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 | 10th Jul, 2018, 06:28: PM

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 | 11th Jul, 2018, 11:23: AM