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ICSE Class 10 Trigonometry — practice questions

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 1–30 of 50.

Match each identity to its short formRead the answer and worked solution →For angle A, what does sin A equal?Read the answer and worked solution →If cos A = 3/5 in a right triangle, what is sec A?Read the answer and worked solution →Find tan 45° × cot 45°.Read the answer and worked solution →Evaluate sin² 30° + cos² 30°.Read the answer and worked solution →At an acute angle A, tan A = 3/4. Find sec A.Read the answer and worked solution →If cot A = 2, find cosec² A.Read the answer and worked solution →Which ratio equals sin 27°?Read the answer and worked solution →A right triangle has adjacent side 8 and hypotenuse 10. Find cos A.Read the answer and worked solution →Evaluate sec 60° − tan 45°.Read the answer and worked solution →A pole casts a 12 m shadow. The sun’s elevation is 45°. Find pole height.Read the answer and worked solution →A tower is 20 m tall. Its top elevation from level ground is 30°. Find horizontal distance.Read the answer and worked solution →A building is 30 m away. Its elevation angle is 45°. Find its height.Read the answer and worked solution →A kite is 40 m above the ground. Its elevation angle is 30°. Find line-of-sight length.Read the answer and worked solution →An aircraft is 600 m above level ground. Depression angle to a point is 30°. Find horizontal distance.Read the answer and worked solution →A 10 m ladder reaches a wall, making 60° with level ground. How high does it reach?Read the answer and worked solution →For acute A, sin A=3/5. Find cos A.Read the answer and worked solution →For 0°≤A<90°, simplify (sec A−tan A)(sec A+tan A).Read the answer and worked solution →For 0°<A≤90°, evaluate (cosec A−cot A)(cosec A+cot A).Read the answer and worked solution →Reduce the quotient tan²A÷sec²A to a single squared ratio; A is acute.Read the answer and worked solution →Rationalising sin A/(1+cos A), for acute A, gives which equivalent fraction?Read the answer and worked solution →For acute A, (1+tan²A)/(1+cot²A) simplifies to?Read the answer and worked solution →Acute A satisfies sec A+tan A=3. Find tan A.Read the answer and worked solution →For acute A, cosec A−cot A=1/2. Find sin A.Read the answer and worked solution →For acute A, (sec²A+cosec²A)/(sec²A cosec²A) equals?Read the answer and worked solution →Factor tan²A−sin²A completely for 0°<A<90°.Read the answer and worked solution →Acute A has sin A+cos A=√(3/2). Find sin A cos A.Read the answer and worked solution →Acute A: tan A+cot A=10/3. What is the sum of squares of these two ratios?Read the answer and worked solution →Which acute angle has equal squared sine and cosine?Read the answer and worked solution →Which angle in 0°≤A≤90° makes sec A undefined?Read the answer and worked solution →

Worked practice questions

Match each identity to its short form

Read exercise and reference answers
Matching pairs
  1. Left
    sin²θ + cos²θ
    Right
    1
  2. Left
    1 + tan²θ
    Right
    sec²θ
  3. Left
    1 + cot²θ
    Right
    cosec²θ
Instructions
Tap a trigonometric expression, then tap the simpler form that it equals.

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For angle A, what does sin A equal?

  1. Adjacent ÷ hypotenuse
  2. Opposite ÷ hypotenuse
  3. Hypotenuse ÷ opposite
  4. Opposite ÷ adjacent
Show answer and solution

Correct answer: B. Opposite ÷ hypotenuse

Sine is the ratio of the opposite side to the hypotenuse.

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If cos A = 3/5 in a right triangle, what is sec A?

  1. 3/5
  2. 5/3
  3. 4/5
  4. 5/4
Show answer and solution

Correct answer: B. 5/3

Secant is the reciprocal of cosine, so sec A = 5/3.

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