Question

find j.
write your answer in simplest radical form.
miles
submit
pythagorean theorem
work it out
not feeling ready yet? these can help:

Explanation:

Step1: Identify trigonometric ratio

We use cosine for the 30° angle: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, where $\theta=30^\circ$, adjacent side = $j$, hypotenuse = $10$ mi.

Step2: Substitute values and solve for $j$

$\cos(30^\circ) = \frac{j}{10}$
We know $\cos(30^\circ) = \frac{\sqrt{3}}{2}$, so substitute:
$\frac{\sqrt{3}}{2} = \frac{j}{10}$
Multiply both sides by 10:
$j = 10 \times \frac{\sqrt{3}}{2}$

Step3: Simplify the expression

$j = 5\sqrt{3}$

Answer:

$5\sqrt{3}$ miles