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Trade Mathematics Course：Angles, right triangles and trigonometry

不限时专题测验：关于Angles, right triangles and trigonometry的15道题，每道题作答后都有解释。每次题目和选项都会重新打乱。

  • 课程
  • 加拿大
  • 90道题
  • 核对于2026年10月13日
  • 事实核查：2026年10月13日
从课文开始Trade Mathematics Course: Lessons：阅读时间约240分钟。测试中的每道题在课文中都有讲解。

专题测验5：Angles, right triangles and trigonometry

  1. 第1题，共15题

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

    答案: C. 55°

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

  2. 第2题，共15题

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

    答案: A. 45°

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

  3. 第3题，共15题

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

    答案: D. 15 ft

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

  4. 第4题，共15题

    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?
    显示答案

    答案: 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. 第5题，共15题

    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?
    显示答案

    答案: 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. 第6题，共15题

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

    答案: C. 7.5 m

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

  7. 第7题，共15题

    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?
    显示答案

    答案: A. 5.81 m

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

  8. 第8题，共15题

    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?
    显示答案

    答案: A. 13 ft

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

  9. 第9题，共15题

    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?
    显示答案

    答案: D. 1.5 m

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

  10. 第10题，共15题

    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?
    显示答案

    答案: C. 424 mm

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

  11. 第11题，共15题

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

    答案: B. 18.4°

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

  12. 第12题，共15题

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

    答案: B. 20 in

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

  13. 第13题，共15题

    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?
    显示答案

    答案: 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. 第14题，共15题

    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.)
    显示答案

    答案: 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. 第15题，共15题

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

    答案: A. 26.6°

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