Source: Questions from Complete International Mathematics For Cambridge IGCSE - David Rayner, Jim Fenson

1. In the cube shown, find:

    a) BD
    b) AS
    c) BS
    d) the angle SBD
    e) the angle ASB.


2. In the wedge shown, PQRS is perpendicular to ABRQ. 
    PQRS and ABRQ are rectangles with AB = QR = 6 m, BR = 4 m, RS = 2 m. Find :

   a) BS
   b) AS
   c) Angle BSR
   d) Angle ASR
   e) Angle PAS

(a)PQRS is perpendicular to ABRQ
Hence SR is perpendicular to BR

(b)ABRQ is a rectangle.
Hence ∠ABR = 90°

3. In the diagram A, B and O are points in a horizontal plane and P is vertically above O.
   OP = h m. A is due West of O, B is due South of O and AB = 60 m. 
   The angle of elevation of P from A is 25° and the angle of elevation of P from B is 33°. a) Find the length AO in terms of h.
 b) Find the length of BO in terms of h.
 c) Find the value of h.

 (a)In △ AOP, ∠AOP = 90°
 (b)In △BPO, ∠BOP = 90°

4. An observer at the top of a tower of height 15 m sees a man due West of him at an angle of depression of 31°. 
    He sees another man due South at an angle of depression 17°. 

  Find the distance between the men.

Let Tower = OA = 15 m
Man due West = P
Angle of depression = 31°
Hence angle with tower = 59°
Man due South = Q
Angle of depression = 17°
Hence angle with tower = 73°
Distance between men = PQ
OP is west and OQ south.
POQ = 90°

5. The figure shows a triangular pyramid on a horizontal base ABC.     V is vertically above B where VB = 10 cm, Angle ABC = 90° and AB = BC = 15 cm. 
    Point M is the mid-point of AC. Calculate the size of angle VMB.

V Is vertically above B.
Hence VBA id perpendicular to ABC