## Three-dimensional Trigonometry Exercise

 1. The figure shows a rectangular prism (cuboid). (a) How many planes are there in this figure? (b) How many vertices? (c) How many edges does the figure have? (d) How many vertical lines? (e) How many of the angles between the edges are right angles? 2. The figure shows a rectangular box. (a) Name the angle between plane PTWS and QVWS?

(b) What is the intersection of line UW and plane VWSQ?

(c) What is the intersection of plane PTUR and plane TUVW?

(d) Which point is the intersection of lines TW and PT?

(e) What is the angle between plane PSWT and plane TUWV?

3. The figure shows a pyramid on a horizontal square base MNOP.

AB is vertical and C is the midpoint of NO.

 (a) Copy the figure. (b) Mark the angle between BP and the plane MNOP. Label this angle x. (c) Draw lines on the figure to show the angle between plane BNO and plane MNOP. Label this angle y. (d) If AB is 9 cm and BP is 11 cm, find the length of AP. (e) If BOA is 67° and BO is 11 cm, find the length of OA. 