Question

find t.
triangle image with 30°, 60°, right angle, side 12√2 km, and t
write your answer in simplest radical form.
blank kilometers

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta=30^\circ$, opposite side is $t$, adjacent side is $12\sqrt{2}$.

Step2: Substitute values into formula

$\tan(30^\circ)=\frac{t}{12\sqrt{2}}$
We know $\tan(30^\circ)=\frac{1}{\sqrt{3}}$, so:
$\frac{1}{\sqrt{3}}=\frac{t}{12\sqrt{2}}$

Step3: Solve for t

Rearrange to isolate $t$:
$t=\frac{12\sqrt{2}}{\sqrt{3}}$
Rationalize the denominator:
$t=\frac{12\sqrt{2}\times\sqrt{3}}{\sqrt{3}\times\sqrt{3}}=\frac{12\sqrt{6}}{3}$

Step4: Simplify the expression

Divide 12 by 3:
$t=4\sqrt{6}$

Answer:

$4\sqrt{6}$ kilometers