Question

solve for ( x ). round to the nearest tenth, if necessary.

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( DEF \), \( \angle E = 90^\circ \), \( \angle D = 18^\circ \), hypotenuse \( DF = 52 \), and \( x \) is the adjacent side to \( \angle D \). So we use cosine: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \).
\( \cos(18^\circ)=\frac{x}{52} \)

Step2: Solve for \( x \)

Multiply both sides by 52: \( x = 52\times\cos(18^\circ) \)
Calculate \( \cos(18^\circ)\approx0.9511 \), then \( x\approx52\times0.9511 \)
\( x\approx49.5 \)

Answer:

\( 49.5 \)