Question

find de.
(there is a right triangle def with right angle at d, angle at e is 60 degrees, hypotenuse ef is 100√2. write your answer in simplified, rationalized form. do not round.
de = )

Explanation:

Step1: Identify trigonometric ratio

We use cosine for $\angle E$:
$\cos(60^\circ) = \frac{DE}{EF}$

Step2: Substitute known values

$EF = 100\sqrt{2}$, $\cos(60^\circ) = \frac{1}{2}$:
$\frac{1}{2} = \frac{DE}{100\sqrt{2}}$

Step3: Solve for DE

Rearrange to isolate $DE$:
$DE = \frac{1}{2} \times 100\sqrt{2}$

Step4: Simplify the expression

Calculate the product:
$DE = 50\sqrt{2}$

Answer:

$50\sqrt{2}$