Question

SOLVE AND SHOW WORK PLSSSS I NEED HELP// Find the length of sides AC, AB, AD, and BD In simplified radical form.

Answer 1

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