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IB Mathematics: Applications and Interpretation SL · 12.10: Geometry & Trigonometry · 12.10.5

Name Date

Angles in 3D shapes Problem set A

Draw the triangle you use. Give angles to 3 significant figures and lengths to 3 significant figures.

Difficulty: first skills applying them stretch

Skills

  1. ABCDEFGH is a cuboid with AB = 7 cm, BC = 4 cm and AE = 5 cm. Find angle FAC.

    7 cm4 cm5 cm?ABCDEFGH

  2. ABCDEFGH is a cuboid with AB = 8 cm, BC = 6 cm and AE = 3 cm. The diagonals AG and EC cross at O. Find the acute angle between AG and EC.

    8 cm6 cm3 cm?ABCDEFGHO

  3. ABCDE is a pyramid. The base ABCD is a square of side 6 cm. Each sloping edge is 10 cm.

    6 cm10 cmBCDEN
    1. (a) Find angle EBC.
    2. (b) Find angle EBD.
    3. (c) Find the height of the pyramid.

  4. ABCDEFGH is a cuboid with AB = 9 cm, BC = 5 cm and AE = 3 cm. Find the angle between the diagonal AG and the base ABCD.

    9 cm5 cm3 cm?ABCDEFGH

  5. ABCDEFGH is a cuboid with AB = 8 cm, BC = 3 cm and AE = 5 cm. Find the angle between the diagonal AG and the face BCGF.

    8 cm3 cm5 cm?ABCDEFGH

In context

  1. A storage crate is a cuboid 120 cm long, 80 cm wide and 60 cm high. A straight rod rests with one end at corner A on the floor and the other at the opposite top corner G.

    120 cm80 cm60 cm?ABCDEFGH
    1. (a) Find the length of the longest rod that fits, which is the diagonal AG.
    2. (b) Find the angle between this rod and the base.

  2. A tent is a square-based pyramid. The square base has side 4 m and each sloping edge is 3.6 m long.

    4 m3.6 mBEN
    1. (a) Find the height of the pyramid.
    2. (b) Find the angle between a sloping edge and the base.

Stretch

  1. A glass ornament is a pyramid ABCD. The base ABC is an equilateral triangle of side 10 cm. The point D is directly above M, the centre of the base, and AD = 14 cm.

    10 cm14 cm?ABCMD
    1. (a) Find the angle between AD and the base.
    2. (b) Find the height DM.

  2. A box has a square base ABCD of side 6 cm. The diagonal AG makes an angle of 35° with the base. Find the height of the box, h.

    6 cm6 cmh35°ABCDEFGH

jmaths.xyz · AI SL · 12.10.5 Angles in 3D shapes