Lesson Worksheet: Trigonometry in Three Dimensions Mathematics

In this worksheet, we will practice solving trigonometry problems in three dimensions.


Using the trigonometric ratios, find tan𝜃.

  • A43
  • B54
  • C34
  • D45
  • E35


A cuboid is shown in the figure. Calculate the angle between 𝐵𝐻 and 𝐻𝐹. Give your answer to two decimal places.


The figure shows a right triangular prism. Find the angle between 𝐴𝐹 and 𝐴𝐶, giving your answer to two decimal places.


A cuboid is shown in the figure. Find the angle between the diagonals 𝐴𝐺 and 𝐸𝐺. Give your answer to two decimal places.


The bearing from point A to a tower positioned at point C is 135. The distance between point A and the tower is 100 m and the elevation of the top of the tower from point A is 20. From point D, the tower is on a bearing of 42, and the bearing of D from A is 160.

Calculate the height of the tower to the nearest tenth.

Calculate the distance AD to the nearest tenth.


In the given cuboid, calculate angle 𝐶𝐶𝐴.


In the given pyramid, calculate angle 𝐴𝐵𝐷 to the nearest degree.


In the given triangular prism, calculate angle 𝐵𝐹𝐶 to the nearest degree.


In the given rectangular prism, calculate, to the nearest degree, the angle between 𝐵𝐷 and plane 𝐴𝐵𝐶𝐷.


In the given figure, calculate the length of 𝐵𝐶.

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