Question

special right triangles!
directions: find each missing side. write all answers in simplest radical form.
use your solutions to navigate through the maze. staple all work to this paper!

Explanation:

Step1: Start at bottom-left triangle

This is a 30-60-90 triangle. In such triangles, the sides follow the ratio $1:\sqrt{3}:2$, where the side opposite $30^\circ$ is the shortest side. Here, the side opposite $60^\circ$ is $12\sqrt{3}$, so let the shortest side (opposite $30^\circ$) be $s$.
$\text{Side opposite }60^\circ = s\sqrt{3} = 12\sqrt{3}$
Solve for $s$: $s = 12$
The hypotenuse $x$ (opposite $90^\circ$) is $2s$:
$x = 2\times12 = 24$
Now, match to the adjacent value: $24$ connects to the triangle with $24\sqrt{6}$ and $60^\circ$.

Step2: Solve 30-60-90 triangle with $24\sqrt{6}$

This is a 30-60-90 triangle where the side opposite $60^\circ$ is $24\sqrt{6}$. Let the shortest side be $s$.
$\text{Side opposite }60^\circ = s\sqrt{3} = 24\sqrt{6}$
Solve for $s$:
$s = \frac{24\sqrt{6}}{\sqrt{3}} = 24\sqrt{2}$
The hypotenuse $x$ is $2s$:
$x = 2\times24\sqrt{2} = 48\sqrt{2}$
Match to adjacent value: $48\sqrt{2}$ connects to the "End!" square.

Answer:

The path through the maze is:

1. Start triangle (bottom-left): $x=24$ → connect to $24$
2. Triangle with $24\sqrt{6}$: $x=48\sqrt{2}$ → connect to "End!"

The final solved values for the path are:

• Starting triangle: $x=24$
• Middle triangle: $x=48\sqrt{2}$