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

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Angles in 3D shapes Problem set B

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

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. ABCDEFGH is a cuboid with AB = 9 cm, BC = 5 cm and AE = 6 cm. Find angle BDE.

    9 cm5 cm6 cm?ABCDEFGH

  2. ABCDEFGH is a cuboid with AB = 9 cm, BC = 4 cm and AE = 5 cm. The diagonals AG and EC cross at O. Find the acute angle between AG and EC.

    9 cm4 cm5 cm?ABCDEFGHO

  3. ABCDE is a pyramid. The base ABCD is a square of side 10 cm. Each sloping edge is 14 cm.

    10 cm14 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 = 8 cm, BC = 7 cm and AE = 4 cm. Find the angle between the diagonal AG and the base ABCD.

    8 cm7 cm4 cm?ABCDEFGH

  5. ABCDEFGH is a cuboid with AB = 8 cm, BC = 4 cm and AE = 3 cm. Find the angle between the diagonal AG and the face CDHG.

    8 cm4 cm3 cm?ABCDEFGH

In context

  1. A wardrobe is a cuboid 150 cm wide, 60 cm deep and 90 cm high. A long curtain pole is put inside with one end at corner A on the floor and the other at the opposite top corner G.

    150 cm60 cm90 cm?ABCDEFGH
    1. (a) Find the length of the longest pole that fits, which is the diagonal AG.
    2. (b) Find the angle between this pole and the base.

  2. A model roof is a square-based pyramid. The square base has side 6 m and each sloping edge is 5.2 m long.

    6 m5.2 mBEN
    1. (a) Find the height of the pyramid.
    2. (b) Find the angle between a sloping edge and the base.

Stretch

  1. A paperweight is a pyramid ABCD. The base ABC is an equilateral triangle of side 12 cm. The point D is directly above M, the centre of the base, and AD = 15 cm.

    12 cm15 cm?ABCMD
    1. (a) Find the angle between AD and the base.
    2. (b) Find the height DM.

  2. A parcel has a square base ABCD of side 8 cm. The diagonal AG makes an angle of 42° with the base. Find the height of the parcel, h.

    8 cm8 cmh42°ABCDEFGH

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