Question

the length of one side of △pty is given. use the relationship between the sides of a 30°-60°-90° triangle to find the lengths of the other two sides. if your answer is $5sqrt{2}$, please type \5sqrt2\ - no space. given pt = 6, complete the table and find the missing sides (radical form)

Explanation:

Step1: Match side to 30-60-90 rule

PT = 6 is opposite 30°, so $x=6$.

Step2: Calculate hypotenuse PY

Hypotenuse = $2x$, so $PY=2\times6=12$.

Step3: Calculate side VT

VT = $x\sqrt{3}$, so $VT=6\sqrt{3}$.

Step4: Fill table values

Map $x, x\sqrt{3}, 2x$ to sides.

Answer:

$30^\circ$	$60^\circ$	$90^\circ$

$PY=12$
$VT=6\sqrt{3}$