3D Trigonometry

 

Question 1:

 

 

ABCDEFGH is a cuboid

The cuboid has
length 17 cm
width 5 cm
height 8 cm

• Calculate the size of angle AHF.

 

 

Question 2:

 

 

 

 

 

ABCD is a horizontal rectangular field.
AB = 50 m.
BC = 27 m.
AT is a vertical mast.

• The angle of elevation of T from B is 19°.
  Calculate the length of AT.
  Give your answer correct to 3 significant figures.
• Calculate the distance from C to T.
  Give your answer correct to 3 significant figures.

 

 

 

Question 3:

 

 

 

Question 4:

 

 

Triangle PQR is a cross section of the prism.
PR = 20 cm
MP = 12 cm
Angle PRQ = 30 degree
Angle PQR = 90 degree

 

• Calculate the size of the angle that the line MR makes with the plane RQLN.

 

 

 

Question 5:

 

ABCDE is a square-based pyramid.

AE = BE = CE = DE = 12 cm
AB = 15 cm

• Calculate the size of angle DEB.

 

 

 

 

Question 6:

 

 

 

 

 

 

Question 6:

 

 

Question 7:

 

 

 

 

Question 8:

 

The diagram shows a triangular prism ABCDEF
AB = 8 cm
BF = 14 cm
EF = 19 cm

 

• Calculate the distance between A and E.
• Calculate the angle between AE and the plane BCEF.