Question

ts 0 submitting an external tool available until oct 2 at 2:25pm

Explanation:

Step1: Identify trig - ratio

In right - triangle $\triangle DEF$ with right - angle at $E$, we know the hypotenuse $DF = 52$ and we want to find the side $DE=x$. The angle $\angle D = 18^{\circ}$. We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos(D)=\frac{DE}{DF}$

Step2: Substitute values

Substitute $\theta = 18^{\circ}$, $DF = 52$ into the cosine formula:
$\cos(18^{\circ})=\frac{x}{52}$

Step3: Solve for $x$

$x = 52\times\cos(18^{\circ})$. Since $\cos(18^{\circ})\approx0.9511$, then $x = 52\times0.9511=49.4572\approx49.46$

Answer:

$49.46$