An engineering team is analyzing a newly plotted topographic map for a proposed mountain road. They observe three distinct features represented by contour lines:

Interpret each of these three contour features and identify what physical landforms they represent.

A drafter is tasked with interpolating 1-meter contours from a grid of spot elevations on a site plan. The grid shows a smooth descent from elevation 105 m down to 98 m. However, the surveyor's field notes indicate that a massive retaining wall (a breakline) runs directly through the middle of the grid, with a top elevation of 104 m and a bottom elevation of 100 m.

Explain why the drafter cannot simply interpolate straight across the grid points, and how the breakline alters the contour map.

A transit is set up at Point A (elevation = $120.00 \text{ m}$). The height of the instrument ($HI$) above Point A is $1.50 \text{ m}$. A reading is taken on a stadia rod held vertically at Point B. The line of sight is inclined upward at an angle of $\theta = +12^\circ 30'$. The stadia interval ($S$) is $1.850 \text{ m}$. The middle hair reading on the rod ($R$) is $2.10 \text{ m}$. The stadia interval factor ($K$) is $100$ and the stadia constant ($C$) is $0.30 \text{ m}$.

Calculate the horizontal distance ($D$) from A to B and the elevation of Point B.

On a topographic map, Point P has a known elevation of $102.4 \text{ m}$ and Point Q has a known elevation of $108.6 \text{ m}$. The horizontal distance measured on the map between P and Q is $62 \text{ mm}$. The contour interval for the map is $2 \text{ m}$.

Determine the exact map distances from Point P to the $104 \text{ m}$, $106 \text{ m}$, and $108 \text{ m}$ contour lines using linear interpolation.

A topographic map has a scale of $1:5000$ and a contour interval of $5 \text{ m}$. The distance measured on the paper map between two adjacent contour lines on a hillside is $8 \text{ mm}$.

Calculate the true ground slope (gradient) of the hillside between these two contours, expressed as a percentage and as an angle.