Question

find $k$.
write your answer in simplest radical form.
$\boldsymbol{square}$ meters

Explanation:

Step1: Identify adjacent side to 60°

Adjacent side: $3\sqrt{3}$ m, hypotenuse = $k$

Step2: Use cosine of 60°

$\cos(60^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(60^\circ) = \frac{1}{2}$, so $\frac{1}{2} = \frac{3\sqrt{3}}{k}$

Step3: Solve for k

Rearrange to isolate $k$:
$k = 2 \times 3\sqrt{3}$
$k = 6\sqrt{3}$

Answer:

$6\sqrt{3}$ meters