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ICSE Class 10 Trigonometry — practice questions — page 2

Explore 50 free Trigonometry questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Trigonometry questions and exercises with answers

Showing questions 31–50 of 50.

Solve sin²A+cos A=1 for 0°≤A≤90°.Read the answer and worked solution →Level ground: eyes 1.5 m high, 10 m from a vertical tower; top elevation 45°. Height?Read the answer and worked solution →Level land: view at ground moves 10 m straight to an upright tower; elevation 30°→60°. Height?Read the answer and worked solution →A 10√3 m vertical tower sees level-ground points on the same ray from its base at depressions 60°,30°. Gap?Read the answer and worked solution →Vertical towers, level bases: 10 m top sees other top/foot at elevation/depression 45°. Other height?Read the answer and worked solution →A 10 m ladder on level ground against a vertical wall changes inclination 60° to 45°. Foot moves out by?Read the answer and worked solution →A broken tree's attached top touches level ground 6 m from its vertical stump, at 30° to ground. Original height?Read the answer and worked solution →A vertical mast's base and tip are at elevations 45°,60° from level ground 10 m horizontally away. Mast length?Read the answer and worked solution →A tower top sees a ground point at depression 35°. Reverse elevation from that point?Read the answer and worked solution →A boat heads straight at constant speed to a vertical cliff: water-level top elevation 30°→60° takes 10 min. Time left?Read the answer and worked solution →Top of a vertical tower has elevations 60° from level ground,30° from 10 m directly above that point. Height?Read the answer and worked solution →Eyes 1.5 m high, vertical tower 31.5 m; level walk straight away from base: tan elevation 0.75→0.5. Walk?Read the answer and worked solution →In an equation written as y = 3 x - 6, the dependent variable isRead the answer and worked solution →If the two lines represented by a pair of linear equations intersect at a single point, the pair hasRead the answer and worked solution →Match each average to its meaningRead the answer and worked solution →Fill the gaps on coordinate geometryRead the answer and worked solution →If the sum of the first $n$ terms of an AP is $S_n=4n-n^2$, what is the $n$th term of the AP?Read the answer and worked solution →Tap every prime numberRead the answer and worked solution →In the word trigonometry, the Greek root 'tri' means:Read the answer and worked solution →An equation true for all values of the variables involved is called an:Read the answer and worked solution →

Worked practice questions

Solve sin²A+cos A=1 for 0°≤A≤90°.

  1. Angle 0° only
  2. No angle solutions
  3. Angle 90° only
  4. Angles 0° and 90°
Show answer and solution

Correct answer: D. Angles 0° and 90°

Substitution gives cos A(1 − cos A) = 0, allowing cosine zero or one at the two endpoints.

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Level ground: eyes 1.5 m high, 10 m from a vertical tower; top elevation 45°. Height?

  1. 15 m
  2. 10 m
  3. 11.5 m
  4. 8.5 m
Show answer and solution

Correct answer: C. 11.5 m

The tower rises 10 tan 45° = 10 m above the eyes, giving total height 11.5 m.

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Level land: view at ground moves 10 m straight to an upright tower; elevation 30°→60°. Height?

  1. 10√3 m
  2. 5√3 m
  3. 10 m
  4. 5 m
Show answer and solution

Correct answer: B. 5√3 m

If the nearer distance is x, x√3 = (x + 10)/√3 gives x = 5 and height 5√3 m.

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