Question

find j.
right triangle with a 60° angle, a 30° angle, right angle, hypotenuse labeled 2√2 mi, and side j opposite 60° angle
write your answer in simplest radical form.
miles

Explanation:

Step1: Identify trigonometric ratio

We use the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta = 60^\circ$, opposite side to $60^\circ$ is $j$, adjacent side is $2\sqrt{2}$.

Step2: Substitute values into ratio

$\tan(60^\circ) = \frac{j}{2\sqrt{2}}$
We know $\tan(60^\circ) = \sqrt{3}$, so:
$\sqrt{3} = \frac{j}{2\sqrt{2}}$

Step3: Solve for $j$

Multiply both sides by $2\sqrt{2}$:
$j = 2\sqrt{2} \times \sqrt{3} = 2\sqrt{6}$

Answer:

$2\sqrt{6}$ miles