SOLUTION: Find the missing lengths. Give your answers in both simplest radical form and as approximations correct to two decimal places. Given: right △RST with RT = 8radical 2 and m�

Question 1193686: Find the missing lengths. Give your answers in both simplest radical form and as approximations correct to two decimal places.
Given: right △RST with
RT = 8radical 2
and m∠
STV = 150°
Find: RS and ST
simplest radical form RS=
approximation RS =
simplest radical form ST =
approximation ST=
Found 2 solutions by parmen, ikleyn:
Answer by parmen(42) (Show Source): You can put this solution on YOUR website!
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.

Answer by ikleyn(52879) (Show Source): You can put this solution on YOUR website!
.
Find the missing lengths. Give your answers in both simplest radical form and as approximations correct to two decimal places.
Given: right △RST with
RT = 8radical 2
and m∠
STV = 150°
Find: RS and ST
simplest radical form RS=
approximation RS =
simplest radical form ST =
approximation ST=
~~~~~~~~~~~~~~~~~~~~~~~~~~

Point "V" is not defined in the problem.

It means that the problem's formulation is FATALLY INCORRECT
and can not be considered as a Math problem.

It is not a subject for discussions.

Throw this "problem" to the closest garbage bin, which is the only right place for it.

Do not post gibberish to this forum.

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