{
  "title": "Word Problems in Trigonometry - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "A ladder 10m long reaches 8m up a wall. What's the angle with ground? 🪜", "options": {"A": "30°", "B": "45°", "C": "53°", "D": "60°"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "A tree's shadow is 15m when sun's elevation is 45°. Tree height? 🌳", "options": {"A": "10m", "B": "15m", "C": "20m", "D": "25m"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "A kite flies at 60m height with 100m string. What's the angle? 🪁", "options": {"A": "30°", "B": "37°", "C": "45°", "D": "53°"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "A 6m ladder makes 60° with ground. How far from wall? 📐", "options": {"A": "2m", "B": "3m", "C": "4m", "D": "5m"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "From top of 30m building, car's angle of depression is 45°. Distance? 🏢", "options": {"A": "20m", "B": "25m", "C": "30m", "D": "35m"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "A flagpole casts 10√3m shadow at 60° sun. Pole height? 🚩", "options": {"A": "10m", "B": "15m", "C": "20m", "D": "30m"}, "correct_answer": "D"},
    {"id": 7, "difficulty": "easy", "question": "A road rises 1m for every 20m horizontal. What's the angle? 🛣️", "options": {"A": "2.86°", "B": "5.74°", "C": "8.53°", "D": "11.31°"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "From boat, 100m cliff top has 30° elevation. Boat's distance? ⛰️", "options": {"A": "100√3m", "B": "100m", "C": "50√3m", "D": "50m"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "A 5m ladder reaches 4m up wall. Ground distance? 🪜", "options": {"A": "2m", "B": "3m", "C": "4m", "D": "5m"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Sun's elevation 30°, shadow 20√3m. Find object height! ☀️", "options": {"A": "10m", "B": "15m", "C": "20m", "D": "25m"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "A ramp rises 2m over 10m length. What's its angle? ♿", "options": {"A": "10°", "B": "11.5°", "C": "15°", "D": "20°"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "From 50m tower, man sees car at 45° depression. Distance? 👀", "options": {"A": "25m", "B": "50m", "C": "75m", "D": "100m"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "A wire supports pole at 60°. If wire is 20m, pole height? 📿", "options": {"A": "10√3m", "B": "15m", "C": "20m", "D": "10m"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Two buildings 50m apart. From top of 30m building, other's top at 30°. Other's height? 🏗️", "options": {"A": "50m", "B": "55m", "C": "58.66m", "D": "60m"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "A slide is 5m long, 3m high. What's its angle? 🛝", "options": {"A": "30°", "B": "37°", "C": "45°", "D": "53°"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "Airplane at 3000m sees airport at 30° depression. Horizontal distance? ✈️", "options": {"A": "1000√3m", "B": "3000√3m", "C": "1500m", "D": "3000m"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "A tree broken at height, top touches ground 10m away at 30°. Original height? 🌴", "options": {"A": "10√3m", "B": "15m", "C": "20m", "D": "25m"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "A road sign says '8% grade'. What's the angle? 📊", "options": {"A": "4.57°", "B": "8°", "C": "10°", "D": "12°"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "From ship, lighthouse at 60° elevation is 100m away. Lighthouse height? 🚢", "options": {"A": "50√3m", "B": "100√3m", "C": "150m", "D": "200m"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "A 12m flagpole's shadow is 4√3m at noon. Sun's elevation? 🕛", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "C"},

    {"id": 21, "difficulty": "medium", "question": "Two poles 20m & 30m high, 50m apart. Find connecting wire's length if straight? 🔌", "options": {"A": "50m", "B": "51m", "C": "52m", "D": "53m"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "From hill top, two cars at 30° & 45° depression, 100m apart vertically. Hill height? 🏞️", "options": {"A": "100(√3+1)m", "B": "50(√3+1)m", "C": "100(√3-1)m", "D": "50(√3-1)m"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "A river's width: from point A, opposite tree at 60°; move 40m back, now 30°. Width? 🌊", "options": {"A": "20√3m", "B": "30m", "C": "40m", "D": "50m"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Cloud at 30° elevation, reflection in lake at 60° depression. Cloud height if lake at 100m? ☁️", "options": {"A": "100m", "B": "150m", "C": "200m", "D": "250m"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "Two towers same height, 60m apart. From midpoint, elevations are 30° & 60°. Height? 🗼", "options": {"A": "15√3m", "B": "20√3m", "C": "25√3m", "D": "30√3m"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "A 1.5m tall boy sees bird at 30°, after 10√3m walk, at 60°. Bird's height? 👦", "options": {"A": "10.5m", "B": "11.5m", "C": "12.5m", "D": "13.5m"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "From top of 75m building, two cars at 30° & 45° depression. Distance between cars? 🏙️", "options": {"A": "75(√3-1)m", "B": "75(√3+1)m", "C": "75m", "D": "150m"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "A pole broken: top touches ground 10m away making 30°. Broken height? 🪵", "options": {"A": "10/√3 m", "B": "20/√3 m", "C": "10√3 m", "D": "20√3 m"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "From lighthouse 100m high, two ships at 30° & 45° depression. Distance between ships? 💡", "options": {"A": "100(√3-1)m", "B": "100(√3+1)m", "C": "100m", "D": "200m"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Balloon rises vertically. From point, after 2 min, angle changes 30° to 60°. Speed? 🎈", "options": {"A": "100√3 m/min", "B": "200√3 m/min", "C": "100/√3 m/min", "D": "200/√3 m/min"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "Two points A & B on ground. From balloon vertically above A, AB at 60°. After rise, at 30°. Height risen? 🎈", "options": {"A": "AB√3", "B": "AB/√3", "C": "AB(√3-1)", "D": "AB(√3+1)"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "From window 10m high, man sees car at 45°, after 10s at 30°. Car's speed? 🚗", "options": {"A": "2(√3-1)m/s", "B": "2(√3+1)m/s", "C": "3(√3-1)m/s", "D": "3(√3+1)m/s"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "A 50m tower's shadow increases by 50m when sun's elevation changes from θ to (90°-θ). Find θ! 🌇", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "From hill, two mileposts at 30° & 45° depression, 1km apart on road. Hill height? ⛰️", "options": {"A": "500(√3+1)m", "B": "500(√3-1)m", "C": "1000(√3+1)m", "D": "1000(√3-1)m"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "A kite's string makes 60° with ground. If string lengthened by 50m, angle becomes 30°. Initial length? 🪁", "options": {"A": "25m", "B": "50m", "C": "75m", "D": "100m"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "From 60m tower, two objects at 30° & 45° depression on same side. Distance between them? 👁️", "options": {"A": "60(√3-1)m", "B": "60(√3+1)m", "C": "30(√3-1)m", "D": "30(√3+1)m"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "A 10√3m tall tree's shadow when sun's elevation is 30°. What's shadow at 60°? 🌳", "options": {"A": "5m", "B": "10m", "C": "15m", "D": "20m"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "From point between two buildings, elevations are 45° & 60°. If buildings 50m apart, heights? 🏢", "options": {"A": "25(3±√3)m", "B": "50(3±√3)m", "C": "75(3±√3)m", "D": "100(3±√3)m"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "A man 1.8m tall sees cloud at 30°. If cloud's reflection in lake at 60° depression, cloud height? ☁️", "options": {"A": "1.8+120m", "B": "1.8+240m", "C": "1.8+360m", "D": "1.8+480m"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Two towers heights ratio 3:1. From midpoint, elevations complementary. Distance ratio? 🏯", "options": {"A": "√3:1", "B": "1:√3", "C": "3:1", "D": "1:3"}, "correct_answer": "A"},

    {"id": 41, "difficulty": "hard", "question": "From top of cliff 200m high, boat at 45°. After 2 min, at 30°. Boat's speed in km/hr? 🚤", "options": {"A": "3(√3-1)km/hr", "B": "6(√3-1)km/hr", "C": "3(√3+1)km/hr", "D": "6(√3+1)km/hr"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "Two pillars equal height, distance 'd' apart. From point between them, elevations α & β. Height? 🏛️", "options": {"A": "d/(cotα + cotβ)", "B": "d/(tanα + tanβ)", "C": "d/(sinα + sinβ)", "D": "d/(cosα + cosβ)"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "From top of tower h m high, line joining two objects has angles α & β below horizontal. Objects distance? 🗼", "options": {"A": "h(cotα ± cotβ)", "B": "h(tanα ± tanβ)", "C": "h(sinα ± sinβ)", "D": "h(cosα ± cosβ)"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "A balloon rises at constant speed. From point, after t seconds, angle changes 30° to 60°. Height gained? 🎈", "options": {"A": "vt√3", "B": "vt/√3", "C": "vt(√3-1)", "D": "vt(√3+1)"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "hard", "question": "From window h m high, car's depression changes from 45° to 30° in t seconds. Car's speed? 🚘", "options": {"A": "h(√3-1)/t", "B": "h(√3+1)/t", "C": "2h(√3-1)/t", "D": "2h(√3+1)/t"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Two towers facing each other. From foot of one, other's top at 60°; from top 30m high, at 30°. Heights? 🏰", "options": {"A": "30m & 60m", "B": "40m & 70m", "C": "45m & 75m", "D": "50m & 80m"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "hard", "question": "A pole broken: upper part makes angle θ with ground, lower part φ with ground. If total length L, broken height? 🪓", "options": {"A": "L sinφ/(sinθ+sinφ)", "B": "L sinθ/(sinθ+sinφ)", "C": "L cosφ/(cosθ+cosφ)", "D": "L cosθ/(cosθ+cosφ)"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "From top of tower 150m high, two cars at 30° & 45° depression on opposite sides. Distance between cars? 🚗", "options": {"A": "150(√3+1)m", "B": "150(√3-1)m", "C": "150m", "D": "300m"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "A kite at height h, string length l. If wind raises it to height 2h with same string length, new angle? 💨", "options": {"A": "sin⁻¹(2h/l)", "B": "cos⁻¹(h/l)", "C": "tan⁻¹(2h/√(l²-4h²))", "D": "2 sin⁻¹(h/l)"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "From point between two vertical poles, angles α & β to tops. If poles heights P & Q, distance from shorter? 🎯", "options": {"A": "P cotα", "B": "Q cotβ", "C": "(P cotα + Q cotβ)/2", "D": "√(PQ cotα cotβ)"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "A man standing x m from building sees top at α; moving y m closer, sees at β. Building height? 🏢", "options": {"A": "x tanα tanβ/(tanβ - tanα)", "B": "y tanα tanβ/(tanβ - tanα)", "C": "(x-y)tanα tanβ/(tanβ - tanα)", "D": "(x+y)tanα tanβ/(tanβ - tanα)"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "hard", "question": "From top of cliff, boat's depression 30°. After 10s, 45°. If speed 10m/s, cliff height? ⛰️", "options": {"A": "100(√3+1)m", "B": "100(√3-1)m", "C": "50(√3+1)m", "D": "50(√3-1)m"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "Two towers heights h1 & h2, distance d apart. From top of each, other's top depression α & β. Prove: d² = h1h2 cotα cotβ 📐", "options": {"A": "True", "B": "False", "C": "Only when α=β", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "A 20m ladder reaches window 16m high on one wall, touches opposite wall at height 8m. Street width? 🏘️", "options": {"A": "12m", "B": "14m", "C": "16m", "D": "18m"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "From top of 75m tower, two objects at 30° & 45° depression on same side. If line joining them makes θ with horizontal, find tanθ! 🎯", "options": {"A": "(√3-1)/(√3+1)", "B": "(√3+1)/(√3-1)", "C": "1/√3", "D": "√3"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "A balloon at height h observed from two points distance d apart on same side, angles α & β. Prove: h = d sinα sinβ/sin(α-β) 🎈", "options": {"A": "True", "B": "False", "C": "Only when β>α", "D": "Cannot prove"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "Two vertical poles 20m & 80m high, 100m apart. Find point on ground where tops subtend equal angle! 🚩", "options": {"A": "40m from shorter", "B": "50m from shorter", "C": "60m from shorter", "D": "70m from shorter"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "From top of 150m tower, helicopter at 30° elevation; after 10s at 60°. Helicopter's speed? 🚁", "options": {"A": "10√3 m/s", "B": "20√3 m/s", "C": "30√3 m/s", "D": "40√3 m/s"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "hard", "question": "A statue on pillar subtends equal angle α at two points distance d apart on ground towards pillar. Pillar height? 🗿", "options": {"A": "d/(2 tanα)", "B": "d tanα/2", "C": "d/(2 sinα)", "D": "d sinα/2"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "From point on ground, flagpole's top at 60°; move 20m towards pole, now 45°. Flagpole height? 🇮🇳", "options": {"A": "20(√3+1)m", "B": "20(√3-1)m", "C": "10(√3+1)m", "D": "10(√3-1)m"}, "correct_answer": "A"}
  ]
}