1. **Problem Statement:** Given a rectangle ABDF with bottom edge FD = 672 m, and angles $\angle CGL = 53^\circ$ and $\angle HJL = 63^\circ$, we want to analyze the geometry of the campus layout. 2. **Understanding the Problem:** - ABDF is a rectangle, so opposite sides are equal and all angles are $90^\circ$. - The bottom edge FD is given as 672 m. - Angles $\angle CGL = 53^\circ$ and $\angle HJL = 63^\circ$ are given for paths between buildings. 3. **Key Formulas and Rules:** - Rectangle properties: $AB = DF$, $AD = BF$, and all angles are $90^\circ$. - Use trigonometric ratios (sine, cosine, tangent) to find lengths or other angles in triangles formed by the paths. 4. **Step-by-step Analysis:** - Since FD = 672 m and ABDF is a rectangle, AB = DF = 672 m. - To find other distances or verify angles, use the given angles and right triangle properties. 5. **Example: Using $\angle CGL = 53^\circ$** - Suppose we want to find the length of CG or GL in triangle CGL. - Use trigonometric ratios: $\sin 53^\circ$, $\cos 53^\circ$, or $\tan 53^\circ$ depending on known sides. 6. **Example: Using $\angle HJL = 63^\circ$** - Similarly, analyze triangle HJL using trigonometric ratios. 7. **Right Triangle AEH:** - The purple path forms a right triangle AEH with right angles at E and H. - Use Pythagoras theorem or trigonometric ratios to find missing lengths if needed. Since the problem does not specify a particular quantity to find, this is the geometric and trigonometric framework to analyze the campus layout. **Final note:** - Use rectangle properties and trigonometry to solve for distances or angles as required.