Calculate the length DP?

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1 Answer
Somebody N.
May 26, 2018

#color(blue)(4.6)#

Explanation:

From diagram:

By Pythagoras' theorem:

#CA=sqrt(4^2+3^2)=5#

#DA=sqrt((CA)^2+2^2)=sqrt(5^2+2^2)=sqrt(29#

#/_BAC=arctan(3/4)#

#/_CAD=arctan(2/5)#

#/_DAB=/_BAC+/_CAD=arctan(3/4)+arctan(2/5)#

#DP=DAsin(/_DAB)#

#DP=sqrt(29)sin(arctan(3/4)+arctan(2/5))=4.6#

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