Practice Maths

Topic Review — Trigonometry

Mixed Practice — L27 – L30

This review covers all lessons in the Trigonometry topic. Try each question before checking your answers.

Review Questions

  1. Naming sides and setting up ratios. Fluency

    1. In a right triangle with θ = 47°, opposite = 9.3, adjacent = 8.7, hypotenuse = 12.7. Write all three trig ratios as fractions (sin, cos, tan).
    2. For each pair of sides, state which trig ratio connects them to angle θ:
      1. Opposite and hypotenuse
      2. Adjacent and hypotenuse
      3. Opposite and adjacent
    3. Write the equation (do not solve): θ = 31°, hypotenuse = 18, find opposite side x.
    4. Write the equation (do not solve): θ = 65°, adjacent = 7, find hypotenuse x.

  2. Find the unknown side. Round to 2 decimal places. Fluency

    1. Angle = 36°, hypotenuse = 20. Find the opposite side.
    2. Angle = 54°, hypotenuse = 15. Find the adjacent side.
    3. Angle = 22°, adjacent = 10. Find the opposite side.
    4. Angle = 68°, opposite = 24. Find the hypotenuse.
    5. Angle = 43°, adjacent = 17. Find the hypotenuse.
    6. Angle = 75°, opposite = 11. Find the adjacent side.

  3. Find the unknown angle. Round to 1 decimal place. Understanding

    1. Opposite = 5, hypotenuse = 13. Find θ.
    2. Adjacent = 7, hypotenuse = 25. Find θ.
    3. Opposite = 9, adjacent = 12. Find θ.
    4. Opposite = 3.6, hypotenuse = 8.4. Find θ.
    5. Adjacent = 14, opposite = 14. Find θ (without a calculator if possible).
    6. A right triangle has sides 8 and 15 (not the hypotenuse). Find the two acute angles.

  4. Elevation, depression, and bearings. Understanding

    1. From a point 65 m from a tree, the angle of elevation to the top of the tree is 38°. Find the height of the tree.
    2. A drone hovers at a height of 55 m. A person on the ground observes the drone at an angle of elevation of 62°. Find the horizontal distance from the person to directly below the drone.
    3. From the top of a 45 m tower, the angle of depression to a car on the ground is 19°. How far is the car from the base of the tower?
    4. A boat sails 90 km on a bearing of 070°. Find the eastward and northward components of its journey.

  5. Multi-step trigonometry problems. Problem Solving

    1. A zip-line runs from a platform 18 m high down to the ground at an angle of depression of 35°.
      1. Find the length of the zip-line.
      2. Find the horizontal distance from the platform to the landing point.
    2. Two observers A and B stand on opposite sides of a flagpole on flat ground. A is 25 m from the base and observes the top at 52° elevation. B observes the top at 38° elevation. Find the distance from B to the base of the flagpole.
    3. A triangular roof truss has a horizontal base of 9 m and the roof rises to a peak at the centre. The angle at each end of the base is 28° (angles of elevation to the peak).
      1. Find the height of the roof at the peak.
      2. Find the length of one sloping side of the truss.
    4. A pilot flying at 3000 m altitude observes two landmarks directly ahead. The angle of depression to Landmark A is 12° and to Landmark B is 28°. Find the distance between the two landmarks.
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