Given that sin(B)=1/5 and AD=BD , find sin(∠ADC).?

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1 Answer
Jim G.
Mar 24, 2018

#sin AhatDC=(4sqrt6)/25#

Explanation:

#"let "angleABD=x" then"#

#angleDAB=xtotriangleABDcolor(blue)" is isosceles"#

#"exterior angle equals sum of opposite interior angles"#

#rArrangleADC=angleABD+angleDAB=2x#

#•color(white)(x)sin^2x+cos^2x=1#

#rArrcosx=sqrt(1-sin^2x)#

#sin(B)=sinx=1/5#

#rArrcosx=sqrt(1-(1/5)^2)#

#color(white)(rArrcosx)=sqrt(1-1/25)=sqrt(24/25)=(2sqrt6)/5#

#•color(white)(x)sin2x=2sinxcosx#

#rArrsinAhatDC=sin2x=2xx1/5xx(2sqrt6)/5=(4sqrt6)/5#

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