Trade Mathematics Course: Angles, right triangles and trigonometry

1. Pergunta 1 de 15

   A right triangle has one angle of 35° (plus the 90° angle). What is the third angle?

   • A45°
   • B145°
   • C55°
   • D65°
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   Resposta: C. 55°

   The angles in a triangle add to 180°. 180 − 90 − 35 = 55°.

2. Pergunta 2 de 15

   Two pieces of trim meet at a 90° outside corner. At what angle do you cut (mitre) each piece?

   • A45°
   • B90°
   • C22.5°
   • D30°
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   Resposta: A. 45°

   Each piece takes half of the corner angle: 90° ÷ 2 = 45°.

3. Pergunta 3 de 15

   A right triangle has legs of 9 ft and 12 ft. How long is the hypotenuse (the longest side)?

   • A13 ft
   • B10.5 ft
   • C21 ft
   • D15 ft
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   Resposta: D. 15 ft

   Pythagoras: c² = a² + b² = 81 + 144 = 225. The square root of 225 is 15 ft.

4. Pergunta 4 de 15

   To check that two walls are square, you mark 6 ft along one wall and 8 ft along the other from the corner. What should the diagonal between the marks measure?

   • A10 ft
   • B9 ft
   • C14 ft
   • D12 ft
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   Resposta: A. 10 ft

   This is the 3-4-5 rule doubled: 6² + 8² = 36 + 64 = 100, and √100 = 10 ft. If the diagonal is 10 ft, the corner is 90°.

5. Pergunta 5 de 15

   You lay out a corner using 1.2 m on one side and 1.6 m on the other. For a true 90° corner, what should the diagonal be?

   • A2.8 m
   • B2.2 m
   • C2.0 m
   • D1.4 m
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   Resposta: C. 2.0 m

   1.2² + 1.6² = 1.44 + 2.56 = 4.00, and √4 = 2.0 m. This is a 3-4-5 triangle scaled by 0.4.

6. Pergunta 6 de 15

   A rectangular form is 6 m by 4.5 m. When it is square, how long is each diagonal?

   • A10.5 m
   • B7.0 m
   • C7.5 m
   • D5.25 m
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   Resposta: C. 7.5 m

   Diagonal = √(6² + 4.5²) = √(36 + 20.25) = √56.25 = 7.5 m. Equal diagonals show the form is square.

7. Pergunta 7 de 15

   A 6 m ladder leans against a wall with its foot 1.5 m from the wall. How high up the wall does it reach, to two decimal places?

   • A5.81 m
   • B6.18 m
   • C4.50 m
   • D5.25 m
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   Resposta: A. 5.81 m

   The ladder is the hypotenuse, so subtract: height = √(6² − 1.5²) = √33.75 = 5.81 m.

8. Pergunta 8 de 15

   A rafter has a run of 12 ft and a rise of 5 ft. How long is the rafter line from the wall to the ridge?

   • A13 ft
   • B11 ft
   • C7 ft
   • D17 ft
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   Resposta: A. 13 ft

   Rafter length = √(12² + 5²) = √(144 + 25) = √169 = 13 ft.

9. Pergunta 9 de 15

   A brace is 2.5 m long. One end is 2.0 m along the floor from the corner. How high up the wall is the other end?

   • A4.5 m
   • B0.5 m
   • C3.2 m
   • D1.5 m
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   Resposta: D. 1.5 m

   Height = √(2.5² − 2.0²) = √(6.25 − 4) = √2.25 = 1.5 m.

10. Pergunta 10 de 15

    A plumber makes a 45° offset to move a pipe over by 300 mm. How long is the diagonal pipe (the travel), to the nearest millimetre?

    • A300 mm
    • B600 mm
    • C424 mm
    • D212 mm
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    Resposta: C. 424 mm

    For a 45° offset, travel = offset × 1.414 (√2). 300 × 1.414 = 424 mm.

11. Pergunta 11 de 15

    A ramp rises 4 ft over a horizontal run of 12 ft. What angle does it make with the ground, to one decimal place?

    • A33.3°
    • B18.4°
    • C19.5°
    • D71.6°
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    Resposta: B. 18.4°

    Use tangent: tan θ = opposite ÷ adjacent = 4 ÷ 12. θ = tan⁻¹(0.333) = 18.4°.

12. Pergunta 12 de 15

    An electrician bends a 10 in offset in conduit using two 30° bends. How far apart are the bends, measured along the conduit?

    • A5 in
    • B20 in
    • C17.3 in
    • D11.5 in
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    Resposta: B. 20 in

    Distance between bends = offset ÷ sin(angle). sin 30° = 0.5, so 10 ÷ 0.5 = 20 in.

13. Pergunta 13 de 15

    A conveyor is 10 m long and set at 20° to the floor. How high does its top end rise above its bottom end, to two decimal places?

    • A3.64 m
    • B9.40 m
    • C3.42 m
    • D2.00 m
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    Resposta: C. 3.42 m

    The conveyor is the hypotenuse and the rise is opposite the angle, so use sine: 10 × sin 20° = 10 × 0.342 = 3.42 m.

14. Pergunta 14 de 15

    You stand 15 m from the base of a tower. The angle up to the top is 40°. How tall is the tower, to two decimal places? (Ignore your eye height.)

    • A12.59 m
    • B17.88 m
    • C11.49 m
    • D9.64 m
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    Resposta: A. 12.59 m

    You know the adjacent side and want the opposite side, so use tangent: 15 × tan 40° = 15 × 0.839 = 12.59 m.

15. Pergunta 15 de 15

    A roof has a pitch of 6 in 12. What is the roof angle, to one decimal place?

    • A26.6°
    • B50.0°
    • C63.4°
    • D30.0°
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    Resposta: A. 26.6°

    tan θ = rise ÷ run = 6 ÷ 12 = 0.5. θ = tan⁻¹(0.5) = 26.6°.

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