Question

solve for x.

x = ? cm
round your answer to the nearest hundredth.

Explanation:

Identify the geometric relationships

Using the Parallel Lines and Alternate Interior Angles knowledge points

$$
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$$

Set up the trigonometric ratio

We have a right triangle where the side adjacent to the \(53^\circ\) angle is \(x\), and the hypotenuse is \(160\text{ cm}\).

$$ \cos(53^\circ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{x}{160} $$

Solve for x

We isolate \(x\) and calculate its value.

$$ x = 160 \cdot \cos(53^\circ) $$

$$ \cos(53^\circ) \approx 0.601815 $$

$$ x \approx 160 \cdot 0.601815 \approx 96.2904 $$

Round to the nearest hundredth

Rounding \(96.2904\) to two decimal places:

$$ x \approx 96.29\text{ cm} $$

Answer:

Solve for x.

\(x =\) <blank>\(96.29\)</blank> cm

Round your answer to the nearest hundredth.