MathClass 10Free printable

Trigonometry

Ratios, standard angles, identities, heights and distances

30 questions · about 60 minutes · answer key included

Name Class Date ⭐ Score / 30

Learn the standard table first; almost every other question uses it. Take A as an acute angle throughout.

Part AComplete the table

Fill in the values. Write "not defined" where needed.

0°30°45°60°90°
sin A
cos A
tan A

Part BEvaluate

  1. sin 30° + cos 60°
  2. 2 tan²45° + cos²30° − sin²60°
  3. sin 60° cos 30° + sin 30° cos 60°
  4. (1 − tan²45°) / (1 + tan²45°)
  5. cos 45° / (sec 30° + cosec 30°)
  6. (sin 30° + tan 45° − cosec 60°) / (sec 30° + cos 60° + cot 45°)

Part CFind the other ratios

  1. If sin A = 3/5, find cos A and tan A.
  2. If tan θ = 8/15, find sin θ and cos θ.
  3. If sec θ = 13/12, find sin θ and tan θ.

Part DProve

  1. (1 − cos²A) cosec²A = 1
  2. (sin θ + cos θ)² = 1 + 2 sin θ cos θ
  3. sin A/(1 + cos A) + (1 + cos A)/sin A = 2 cosec A

Part EHeights and distances

Draw a neat diagram for each. Use √3 = 1.732 where needed.

  1. 🗼 From a point 30 m from the foot of a tower, the angle of elevation of its top is 30°. Find the height of the tower.
  2. 🪁 A kite is flying on a 60 m string that makes an angle of 60° with the ground. How high is the kite? (Assume the string is straight.)
  3. 🪜 A ladder leans against a wall and makes an angle of 60° with the ground. Its foot is 2.5 m from the wall. Find the length of the ladder.

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