Question

solve for x.

image of a right-angled triangle with a horizontal base of length 130 cm, a hypotenuse labeled x, and an angle of depression of 24 degrees from a horizontal dashed line at the top vertex.

\\(x = ?\text{ cm}\\)

round your answer to the nearest hundredth.

Explanation:

Identify the angle of elevation

Using the Parallel Lines and Alternate Interior Angles knowledge points

$$ \theta = 24^\circ $$

Set up the trigonometric ratio

Using the Trigonometric Ratios and Right Triangle Trigonometry knowledge points

$$ \cos(24^\circ) = \frac{130}{x} $$

Solve for x

Using the Right Triangle Trigonometry knowledge point

$$
LATEXBLOCK0
$$

Round to the nearest hundredth

Using the Right Triangle Trigonometry knowledge point

$$ x \approx 142.30 $$

Answer:

Solve for x.
\(x =\) <blank>\(142.30\)</blank> cm
Round your answer to the nearest hundredth.