Question

the length of one side of \\(\triangle ptv\\) is given. use the relationship between the sides of a \\(30^\circ\\)-\\(60^\circ\\)-\\(90^\circ\\) triangle to find the lengths of the other two sides.\
if your answer is \\(5\sqrt{2}\\), please type \5sqrt2\ - no space.\
given \\(pv = 18\\). complete the table and find the missing sides (radical form).

Explanation:

Step1: Identify hypotenuse and solve for $x$

The hypotenuse $PV=2x=18$, so $x=\frac{18}{2}=9$.

Step2: Fill table for 30° side

Side opposite 30° is $x=9$.

Step3: Fill table for 60° side

Side opposite 60° is $x\sqrt{3}=9\sqrt{3}$.

Step4: Fill table for 90° side

Side opposite 90° is $2x=18$.

Step5: Match sides to triangle

$PT$ (opposite 30°) = 9; $VT$ (opposite 60°) = $9\sqrt{3}$.

Answer:

Table:

30°	60°	90°

Missing Sides:

$PT = 9$
$VT = 9sqrt3$