Lesson Worksheet: Trigonometry in Three Dimensions Mathematics

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

Question 1

Using the trigonometric ratios, find tan𝜃.

  • A43
  • B54
  • C34
  • D45
  • E35

Question 2

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

Question 3

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

Question 4

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

Question 5

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.

Question 6

In the given cuboid, calculate angle 𝐶𝐶𝐴.

Question 7

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

Question 8

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

Question 9

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

This lesson includes 45 additional question variations for subscribers.

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