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Ecolint Campus des NationsMathématiques
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Pack B — Fluency

Ecolint Campus des NationsMathematics
Year 9 · 9.3 Right-angle Trigonometry

Pack B · Fluency

Name: _________________________________
Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10
  1. 1.
    In a right-angled triangle, the angle θ\theta has opposite side 8 cm and hypotenuse 17 cm. Write down sin⁡θ\sin \theta as a fraction in its simplest form.
     
  2. 2.
    Identify the opposite, adjacent, and hypotenuse for angle 30° in a right-angled triangle with hypotenuse 10 cm.
     
  3. 3.
    Find sin 60° in surd form.
     
  4. 4.
    A right triangle has opposite 5 and adjacent 12. Find tan θ.
     
  5. 5.
    In a right triangle, sin⁡θ=0.6\sin \theta = 0.6 and hypotenuse = 10. Find the opposite side.
     
  6. 6.
    Use sin⁡30°=0.5\sin 30° = 0.5 to find the opposite side when angle = 30° and hyp = 8 cm.
     
  7. 7.
    Find tan⁡45°\tan 45° exactly.
     
  8. 8.
    A right triangle has hypotenuse 10 and an angle 30°. Find the side opposite the 30° angle.
     
  9. 9.
    Find tan 30° exactly.
     
  10. 10.
    A right triangle has hyp 13 and one leg 12. Find the third side, and then sin⁡θ\sin \theta for the angle opposite the 5-side.
     
SilverQuestions 11–20
  1. 11.
    In a right triangle, the side opposite θ\theta is 7 cm and hyp = 15 cm. Find θ\theta to 1 d.p.
     
  2. 12.
    A right triangle has hyp 12 cm and angle 50°. Find the opposite side to 2 d.p.
     
  3. 13.
    A right triangle has adjacent 5 cm and angle 45°. Find the opposite side to 2 d.p.
     
  4. 14.
    A right triangle has adjacent 6 and opposite 8. Find (a) the hypotenuse, (b) the angle θ to 1 d.p.
     
  5. 15.
    Find the angle of elevation: a tree casts a 12 m shadow when the tree is 7.5 m tall.
     
  6. 16.
    A right triangle has hyp 10 and angle 30°. Find the adjacent (to 2 d.p.).
     
  7. 17.
    A ladder of length 5 m leans against a wall, making a 60° angle with the ground. Find the height up the wall.
     
  8. 18.
    A right triangle has opposite 8 and adjacent 15. Find (a) the angle θ to 1 d.p., (b) the hypotenuse.
     
  9. 19.
    A 25 m vertical building. From the top, the angle of depression to a car is 20°. Find the horizontal distance.
     
  10. 20.
    Find the angle in a right triangle with hyp 13 and opposite 5.
     
GoldQuestions 21–30
  1. 21.
    A vertical tree casts a shadow of 15 m on horizontal ground. The angle of elevation from the tip of the shadow to the top of the tree is 48°. Find the tree height to 2 d.p.
     
  2. 22.
    A cuboid has length 8 cm, width 6 cm, height 4 cm. Find the angle between the space diagonal and the base.
     
  3. 23.
    A right triangle has angle 30° and hyp 8 cm. Use exact values to find the opposite and adjacent.
     
  4. 24.
    An aircraft's angle of approach to a runway is 3°. How high should it be when 7 km away horizontally? Give in m.
     
  5. 25.
    A right triangle has hyp 10 and one acute angle 35°. (a) Find the opposite and adjacent. (b) Find the area.
     
  6. 26.
    Find xx in: angle in a right triangle is (x+10)°(x + 10)° and the opposite/adjacent ratio is 1.
     
  7. 27.
    A right triangle has one acute angle of 25° and hypotenuse 20 cm. Find the perimeter to 2 d.p.
     
  8. 28.
    Two right-angled triangles share a common leg. The first has opposite 3 and adjacent 4. The second has opposite 5 and the same adjacent 4. Find the difference in their hypotenuses.
     
  9. 29.
    A right triangle has hyp 25 cm and an angle 60° at one acute vertex. Find the lengths of the two legs.
     
  10. 30.
    A boat sails 10 km on bearing 030°. (a) How far north? (b) How far east?
     
PlatinumQuestions 31–40
  1. 31.
    PQRS is a square base 8 cm; pyramid apex V is 12 cm above the centre. M = midpoint of QR. Find (a) GM (G = centre), (b) VM, (c) angle of face VQR with the base.
     
  2. 32.
    In a right triangle, the angle at A is 30° and the hypotenuse is 12 cm. Use exact values to find the legs.
     
  3. 33.
    A cliff of height hh stands on level ground. From point A, 28 m from the base, line of sight to the top is 52 m. From B further, sight is 60 m. Find hh and the distance from B to the base.
     
  4. 34.
    A flagpole is observed from two points 50 m apart. From the closer point, elevation = 35°. From the further, 22°. Find the height of the flagpole.
     
  5. 35.
    A ladder of length 6 m leans against a wall. The angle with the ground is initially 70°; it slips to 60°. By how much does the top descend?
     
  6. 36.
    Find sin⁡75°\sin 75° exactly using the identity sin⁡(45°+30°)=sin⁡45cos⁡30+cos⁡45sin⁡30\sin(45° + 30°) = \sin 45 \cos 30 + \cos 45 \sin 30.
     
  7. 37.
    A triangular prism has a right-angled triangular cross-section with legs 6 and 8 cm. The hypotenuse is the base of the prism, lying on a table. Find the angle the prism's slanted face makes with the table.
     
  8. 38.
    A square pyramid has slant edge from base vertex to apex = 13 cm and base diagonal half-length = 5 cm. Find the apex height above the centre.
     
  9. 39.
    A skier descends a 100 m slope inclined at 15° to horizontal. Find (a) horizontal distance covered, (b) vertical drop.
     
  10. 40.
    A 3D Pythagoras-with-trig problem: a square pyramid has base side 10 cm and slant edge 13 cm. Find the angle between a slant edge and the base.