Answer:
[tex]b=3\sqrt{13}[/tex]
Step-by-step explanation:
Segment Addition Postulate:
[tex]\bar{PY}=\bar{MP}+\bar{MY}[/tex]
Substitute MP = 4, MY = 9 into PY = MP + MY:
[tex]\bar{PY}=4+9[/tex]
Calculate PY = 4 + 9:
[tex]\bar{PY}=13[/tex]
Representing same angles:
[tex]cos A = leg adjacent to <A/hypotenuse:
[tex]cos(Substitute DY = b, PY = 13 into cos (<DYP)=DY/PY:
[tex]cos(Substitute <DYP=<DYM into cos(<DYP)=b/13:
[tex]cos(cos A=leg adjacent to <A/hypotenuse:
[tex]cos\left(Substitute DY=b, MY=9, cos(<DYM)=b/13 into cos (<DYM)=MY/DY:
[tex]\frac{b}{13}=\frac{9}{b}[/tex]
Calculate b/13=9/b:
[tex]b=3\sqrt{13}[/tex]
I hope this helps you :)
