Question 1193686
Certainly, let's find the missing lengths in the right triangle RST.

**1. Analyze the Given Information**

* We have a right triangle RST, which implies that ∠RTS = 90°.
* RT = 8√2 
* m∠STV = 150° 

**2. Determine ∠RST**

* Since ∠STV = 150° and ∠RTS = 90°, 
* ∠RST = 180° - ∠STV - ∠RTS = 180° - 150° - 90° = -60° 

* However, angles in a triangle cannot be negative. This suggests there might be an error in the given information. 

**3. Assuming a Corrected Angle**

Let's assume that m∠STV = 30° instead of 150°. This would make more sense in the context of a right triangle.

* ∠RST = 180° - ∠STV - ∠RTS = 180° - 30° - 90° = 60°

**4. Find RS and ST using Trigonometric Ratios**

* Since ∠RST = 60° and ∠RTS = 90°, ∠SRT = 30° 

* **Find RS (hypotenuse):**
    * cos(∠SRT) = RS / RT
    * cos(30°) = RS / (8√2)
    * RS = 8√2 * cos(30°)
    * RS = 8√2 * (√3/2)
    * **RS = 4√6** 
    * **RS ≈ 9.80**

* **Find ST (opposite side to ∠SRT):**
    * sin(∠SRT) = ST / RT
    * sin(30°) = ST / (8√2)
    * ST = 8√2 * sin(30°)
    * ST = 8√2 * (1/2)
    * **ST = 4√2**
    * **ST ≈ 5.66**

**Therefore:**

* **simplest radical form RS = 4√6**
* **approximation RS ≈ 9.80**
* **simplest radical form ST = 4√2**
* **approximation ST ≈ 5.66**

**Note:** 

* Please double-check the given value of ∠STV. If it is indeed 150°, the calculations will need to be adjusted accordingly. 
* This solution assumes that ∠STV = 30° for a valid solution within the context of a right triangle.