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The image below shows an ammonium ion which has the shape of a regular tetrahedron - Leaving Cert DCG - Question A-3 - 2021
Question A-3
The image below shows an ammonium ion which has the shape of a regular tetrahedron. A Nitrogen atom is located at the centre of the tetrahedron and four Hydrogen ato... show full transcript
Worked Solution & Example Answer:The image below shows an ammonium ion which has the shape of a regular tetrahedron - Leaving Cert DCG - Question A-3 - 2021
Step 1
Determine the dihedral angle between the planes ABC and ABD.
Answer
To find the dihedral angle between the planes ABC and ABD,
- Identify the line of intersection, AB. We first consider the projections of the planes on the auxiliary view.
- Let Y1 be a point parallel to the line of intersection AB. The projections of the planes ABC and ABD on the Y1 auxiliary view will show how these planes relate to each other.
- Establish X2 as the perpendicular from point A to the line AB in the auxiliary view.
- The edge views of planes ABC and ABD on X2Y2 help visualize their spatial orientation.
- Finally, applying trigonometric principles or measuring directly from the projections will yield the required dihedral angle.
Step 2
Determine the true angle between the lines BN and CN.
Answer
To calculate the true angle between the lines BN and CN, we need to:
- Construct triangle BCN and determine its true shape using a proper projection method. This will involve extracting the necessary lengths and angles from the existing geometric configuration.
- Identify the angle of interest, which is the angle between the lines BN and CN, from the derived triangle.
- The accurate measurement or calculation will provide the required true angle between lines BN and CN.