# 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 . 