Question

the length of one side of △prt 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 5√2, please type \5sqrt2\ - no space. given pt = 4. complete the table and find the missing sides. (radical form)

Explanation:

Step1: Match side to 60° value

Given $PT = 4$, which corresponds to the $x\sqrt{3}$ side (opposite 60°). Solve for $x$:
$$x = \frac{4}{\sqrt{3}} = \frac{4\sqrt{3}}{3}$$

Step2: Find side for 30° angle

The side opposite 30° is $x$, so substitute $x$:
$$VT = \frac{4\sqrt{3}}{3}$$

Step3: Find hypotenuse (90° side)

The hypotenuse is $2x$, so substitute $x$:
$$PV = 2\times\frac{4\sqrt{3}}{3} = \frac{8\sqrt{3}}{3}$$

Step4: Fill table values

Map each angle to its side length:

• 30°: $\frac{4\sqrt{3}}{3}$
• 60°: $4$
• 90°: $\frac{8\sqrt{3}}{3}$

Answer:

Table:

30°	60°	90°

Missing Sides:

$VT = \frac{4\sqrt{3}}{3}$
$PV = \frac{8\sqrt{3}}{3}$