Some Applications of Trigonometry
20 solved questions from Class 10 Mathematics, each with the full working. Tap any question to see the step-by-step solution.
- 1 From a point on the ground, the angle of elevation of the top of a telephone pole is 30°. If the horizontal distance from the point to the foot of the pole is 10√3 m, what is the height of the pole? easy MCQ 1 mark Height from angle of elevation
- 2 In triangle ABC, side a = 8 cm, side b = 10 cm and the included angle C = 60°. Find the length of side c (correct to two decimal places). hard MCQ 3 marks Cosine rule to find a side
- 3 A street light is fixed at the top of a pole. From a point on the ground 30 m away from the pole, the angle of elevation of the light is 35°. A man 1.8 m tall stands between the pole and the point, casting a shadow of length 8 m on the ground. Find the height of the pole. medium 2 marks Height from angle of elevation with extra data
- 4 A cliff overlooks the sea. From a point on the cliff, the angle of depression to a boat is 25°. If the horizontal distance of the boat from the base of the cliff is 200 m, find the height of the cliff. medium 3 marks Height of cliff using angle of depression
- 5 A lamp is placed at the top of a pole. When a man of height 1.5 m stands 12 m away from the pole, the angle of elevation of the lamp from the man's eyes is 25°. Find the height of the pole. (Take the man's eye level at 1.5 m above the ground.) medium MCQ 2 marks Height of pole using angle of elevation
- 6 Find the area of a triangle whose two sides are a = 7 cm and b = 9 cm and the included angle C = 30°. easy 1 mark Area of triangle (SAS)
- 7 In a right‑angled triangle, the angle at the base is 35° and the side opposite this angle is 15 m. Find the length of the hypotenuse. hard MCQ 5 marks Finding hypotenuse (trigonometric ratios)
- 8 What is the value of sin 30°? medium MCQ Trigonometric Values
- 9 What is the value of cos 0°? medium MCQ Trigonometric Values
- 10 Simplify: sin² θ + cos² θ. medium MCQ Trigonometric Identities
- 11 What is tan 45° equal to? medium MCQ Trigonometric Values
- 12 If sin A = 3/5 in a right triangle, what is cos A? medium MCQ Trigonometric Ratios
- 13 What is 1 + tan² θ equal to? medium MCQ Trigonometric Identities
- 14 Find sec 60°. medium MCQ Trigonometric Values
- 15 What is the value of sin 90°? medium MCQ Trigonometric Values
- 16 A ladder 10m long touches a wall at height 5m. Find angle of elevation. medium MCQ Applications of Trigonometry
- 17 Simplify: sin (90° - A). medium MCQ Complementary Angles
- 18 What is the domain, range, or fundamental theorem introduced in 'Some Applications of Trigonometry' (Class 10 Mathematics)? medium MCQ Functions & Theorems
- 19 What is the derivative or integral formula associated with 'Some Applications of Trigonometry'? medium MCQ Calculus & Formulae
- 20 How do you find the solution set or optimum value in 'Some Applications of Trigonometry'? medium MCQ Problem Solving & Optimization