Worksheet: Angle between Two Planes

In this worksheet, we will practice finding the measure of the angle between two planes.

Q1:

Find, to the nearest second, the measure of the angle between the planes 9 𝑥 6 𝑦 + 5 𝑧 = 8 and 2 𝑥 + 2 𝑦 + 7 𝑧 = 8 .

  • A 4 8 3 1 3 7
  • B 6 5 1 1 2 9
  • C 7 5 6 5 9
  • D 8 6 4 8 5 1

Q2:

Find, to the nearest second, the measure of the angle between the planes ( 5 , 9 , 4 ) 𝑟 = 6 and 4 𝑥 𝑦 6 𝑧 = 3 .

  • A 4 6 3 7 2 1
  • B 6 3 5 4
  • C 7 4 9 5 9
  • D 8 6 2 6 6

Q3:

In the figure, suppose that 𝐴 𝐵 = 2 8 , 𝐵 𝐷 plane 𝐵 𝐴 𝐶 , and 𝐷 𝐸 𝐴 𝐶 . Find the length of 𝐷 𝐸 .

  • A 7 6 5
  • B25.24
  • C 2 1
  • D 7 5

Q4:

In triangle 𝐴 𝐵 𝐶 , 𝑚 𝐴 = 6 0 and 𝐴 𝐵 = 2 4 . 𝐵 𝐷 is a normal to the plane 𝐴 𝐵 𝐶 , and 𝑂 the foot of the perpendicular from 𝐷 to 𝐴 𝐶 . If 𝐷 𝑂 = 7 2 , determine the length of 𝐵 𝐷 .

  • A 1 2 3 5
  • B 1 2 3 9
  • C 4 8 2
  • D 1 2 3 3

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