Answer:
AC=27
AB=9√3
AD=27
BD=18√3
Step-by-step explanation:
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We can find side AB by using the sine property of Pythagorean theorem
sin(30°)=AB/18√3
AB=18√3sin30° but sin(30)=½
Therefore AB=18√3×½=9√3
Using Triangle ABC, Pythagorean theorem helps us find AC
(18√3)²=(9√3)²+AC²
972=243+AC²
972-243=AC²
729=AC² (find the square root of both sides)
√729=AC
AC=27
To find AD,
tan(30°)=AB/AD but AB=9√3
tan30=9√3/AD and tan30=√3/3
√3/3=9√3/AD simplify
AD=27
Finally,
BD=√(9√3)²+(27)²
BD=√243+729
BD=√972=18√3
