Theorem of three perpendiculars
A standard method from Trigonometry in 3-D: the steps and worked examples.
Steps
If PN is perpendicular to a plane, and NM (in the plane) is perpendicular to a line ℓ in the plane, then PM is also perpendicular to ℓ.
Why it helps: it tells you which line in the sloping plane is perpendicular to the line of intersection, so you can find the angle between planes with a right triangle.
Worked examples
Example 1: Angle between two planes (theorem of three perpendiculars): in the same cuboid, find the angle between the plane ABGH and the base.
line of intersection: AB
in the base, BC ⊥ AB
GC ⊥ base and BC ⊥ AB, so GB ⊥ AB (three perpendiculars)
the angle is ∠GBC
tan ∠GBC = 5/6
∠GBC ≈ 39.8°For the whole topic, read Trigonometry in 3-D: key points, common mistakes and how the DSE tests it.