Question

question 2

if \\(c = 6\\), find the value of \\(x\\) to the nearest tenth.

\\(x =\\) ______ (type your answer in blank 1)

blank 1:

Explanation:

Identify the given values and target variable

We are given a right-angled triangle with:

• Hypotenuse \(c = 6\)
• An angle of \(30^\circ\) opposite to the side labeled \(x\)
• An angle of \(60^\circ\) adjacent to the side labeled \(x\)
• We need to find the value of \(x\) to the nearest tenth.

Apply trigonometric ratios

Using the definition of the sine ratio for the \(30^\circ\) angle:

$$ \sin(30^\circ) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{x}{c} $$

Substitute the known values and solve for x

Substitute \(c = 6\) and \(\sin(30^\circ) = 0.5\):

$$ 0.5 = \frac{x}{6} $$

$$ x = 6 \cdot 0.5 = 3 $$

Round to the nearest tenth

The value of \(x\) is exactly \(3\), which can be written to the nearest tenth as \(3.0\).

Answer:

If \(c = 6\), find the value of x to the nearest tenth.
\(x =\) <blank>3.0</blank> (type your answer in Blank 1)