3D Pythagoras & Trigonometry (CIE IGCSE Maths: Extended)

Calculate angle BEC.

Angle BEC = ...................................................

The point G lies on the line ED and GD = 7 cm.

Work out angle BGE.

Angle BGE = ................................................

The diagram shows a field, ABCD, on horizontal ground.

The diagram shows an open box  in the shape of a cuboid.
 cm,  cm and  cm.
A thin rod rests partly in the box as shown.
The rod is  cm long.

Calculate , the length of the rod which is outside the box.

............................................ cm

Calculate the angle the rod makes with the base of the box.

The diagram shows a cuboid .

Calculate the volume of the cuboid.
Give your answer correct to significant figures.

The diagram shows a pyramid.

is a square with sides of length 10 cm.
The other faces of the pyramid are equilateral triangles with sides of length 10 cm.

Calculate the volume of the pyramid.
Give your answer correct to 3 significant figures.

Find the size of angle .

The diagram shows a prism with a rectangular base, ABFE.
The cross-section, ABCD, is a trapezium with AD = BC.
AB = 8 cm, GH = 5 cm, BF = 12 cm and angle ABC = 70°.

The perpendicular from G onto EF meets EF at X. 

ABCDEFGH is a cuboid.
AB = 8 cm, BC = 5 cm and CG = 11 cm.

Ivana has a pencil of length 13cm.

Does this pencil fit completely inside the cuboid?
Show how you decide.

The diagram shows a pyramid with a square base ABCD.
DB = 8 cm.
P is vertically above the centre, X, of the base and PX = 5 cm.

Calculate the angle between PB and the base ABCD.

The diagram shows a solid prism .

The trapezium , in which is parallel to , is a cross section of the prism.
The base of the prism is a horizontal plane.
and are rectangles.
The midpoint of is vertically above the midpoint of so that .

The perpendicular distance between edges and is 20 .

Calculate the size of the angle between and the plane .
Give your answer correct to one decimal place.

The diagram shows a solid pyramid  with a horizontal base.

The base, , of the pyramid is a square of side 10 .

The vertex  of the pyramid is vertically above the centre  of the base so that  

The total surface area of the pyramid is 360 

Work out the size of the angle between  and the base .
Give your answer correct to 3 significant figures.

Alvin has a crate in the shape of a cuboid.
The crate is open at the top.
The internal dimensions of the crate are 46cm long by 46cm wide by 55cm high.

Alvin has a stick of length 95cm.
Alvin places the stick in the crate so that the shortest possible length extends out above the top of the crate.

Calculate the length of the stick that extends out of the crate.

..................................................... cm

Calculate the angle the stick makes with the base of the crate.