The image on the right shows a piece of roadside sculpture, in the form of a steel hedgehog, which is located on the M11 in Co - Leaving Cert DCG - Question B-3 - 2018

To find the dihedral angle, first identify the line of intersection (L) between planes ABC and ABDE. Then:

1. Construct a line perpendicular to the plane ABC from point A using the normal vector.
2. Similarly, create a perpendicular from point A to plane ABDE.
3. Measure the angle between these two perpendicular lines using trigonometric relations:

heta = an^{-1} rac{h_1}{h_2} where $h_1$ and $h_2$ are the distances along the respective lines.

To visualize point G accurately:

1. Plot point G at coordinates (175, 125, 10) in both plan and elevation views.
2. To calculate the distance from G to B, which is at (210, 35, 80), utilize the distance formula:

$d = ext{sqrt}((x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2)$

Substituting the values: $d = ext{sqrt}((210 - 175)^2 + (35 - 125)^2 + (80 - 10)^2)$ Evaluate this to obtain the distance.

From point C, draw a horizontal line extending to the plane AEFG:

1. Mark the point where this line meets the plane AEFG at a distance of 55 mm from C.
2. Indicate this intersection in both the plan and elevation views as C'.
3. The angle between the horizontal section and vertical plane (VP) can be calculated by examining the elevation, using the geometrical relation:

ext{angle} = an^{-1} rac{ ext{opposite}}{ ext{adjacent}} Define the lengths accordingly to find the angle.