# Lesson Worksheet: Trigonometry in Three Dimensions Mathematics

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

**Q1: **

Using the trigonometric ratios, find .

- A
- B
- C
- D
- E

**Q2: **

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

**Q3: **

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

**Q4: **

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

**Q5: **

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

Calculate the height of the tower to the nearest tenth.

Calculate the distance AD to the nearest tenth.

**Q6: **

In the given cuboid, calculate angle .

**Q7: **

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

**Q8: **

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

**Q9: **

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

**Q10: **

In the given figure, calculate the length of .