Question

solve for x. round to the nearest tenth, if necessary. triangle image with right angle at d, side cd = 6.6, angle at e is 73°, side de = x

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle $\triangle CDE$ with right angle at $D$, $\angle E = 73^\circ$, hypotenuse $CE = 6.6$, and adjacent side $DE = x$ to $\angle E$. Use cosine:
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(73^\circ) = \frac{x}{6.6}$

Step3: Solve for $x$

Rearrange to isolate $x$:
$x = 6.6 \times \cos(73^\circ)$
Calculate $\cos(73^\circ) \approx 0.2924$, so:
$x \approx 6.6 \times 0.2924$

Step4: Compute final value

$x \approx 1.93$
Round to nearest tenth: $x \approx 1.9$

Answer:

$1.9$