Questions: Find the length of RX

Transcript text: Find the length of $\overline{R X}$

Solution

Solution Steps

Step 1: Identify the given information

We are given a right triangle $ \triangle URX $ with:

$ \angle X = 6^\circ $
$ UR = 8 $ (hypotenuse)
$ \angle R = 90^\circ $

Step 2: Use trigonometric ratios

To find the length of $ RX $, we can use the sine function, which relates the angle to the opposite side and the hypotenuse: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]

Step 3: Apply the sine function

For $ \angle X = 6^\circ $: \[ \sin(6^\circ) = \frac{RX}{UR} \] \[ \sin(6^\circ) = \frac{RX}{8} \]

Step 4: Solve for $ RX $

\[ RX = 8 \cdot \sin(6^\circ) \]

Step 5: Calculate the value

Using a calculator to find $ \sin(6^\circ) $: \[ \sin(6^\circ) \approx 0.1045 \] \[ RX = 8 \cdot 0.1045 \approx 0.836 \]

Final Answer

The length of $ RX $ is approximately $ 0.836 $.

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