The image on the right shows a playground unit incorporating two planar surfaces which intersect as shown to represent the bow of a boat - Leaving Cert DCG - Question B-2 - 2017

The dihedral angle can be determined by first identifying the line of intersection AB. Project the points from each plane onto a common view to visualize the angle formed between them. Apply the formula for the dihedral angle, which is found using the cosine of the angle between the normals of the two planes. Specifically:

$heta = an^{-1} \left( \frac{h_2 - h_1}{d} \right)$

Where, ( h_1 ) and ( h_2 ) are heights at points, and ( d ) is the horizontal distance.

To determine the true shape of surface ABCD, project points A, B, C, and D onto a true shape view. Include a circular porthole, ensuring its center is positioned 30mm from line AB and 50mm from point D. The circle should be accurately drawn with a diameter of 20mm within the true shape view of ABCD.

Calculate the midpoints of lines AB, AD, and EF using the midpoint formula:

$P_{mid} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right)$

After obtaining the midpoints, draw the oblique plane representing the seat in both the elevation and plan views. Clearly indicate the necessary horizontal and vertical traces for this plane.