{
  "title": "Angles of Elevation & Depression - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "An observer looks at a bird 🐦 on a tree. The angle from the horizontal line UP to the line of sight is called?", "options": {"A": "Angle of Depression", "B": "Angle of Inclination", "C": "Angle of Elevation", "D": "Right Angle"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Looking down from a balcony at a car 🚗, the angle formed is?", "options": {"A": "Angle of Elevation", "B": "Acute Angle", "C": "Angle of Depression", "D": "Obtuse Angle"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "If the angle of elevation to a kite 🪁 is 30°, what is the angle of depression FROM the kite to the observer?", "options": {"A": "30°", "B": "60°", "C": "150°", "D": "90°"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "From a point on the ground, the top of a tower 🗼 appears at 45°. This is an angle of?", "options": {"A": "Reflection", "B": "Elevation", "C": "Depression", "D": "Rotation"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "A pilot ✈️ looks down at a runway. The angle measured is?", "options": {"A": "Angle of Elevation", "B": "Angle of Depression", "C": "Angle of Projection", "D": "Straight Angle"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Angle of elevation and angle of depression are always?", "options": {"A": "Equal", "B": "Complementary", "C": "Supplementary", "D": "Vertically Opposite"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "The line drawn from the eye of the observer to the object is called?", "options": {"A": "Horizontal Line", "B": "Line of Sight 👀", "C": "Vertical Line", "D": "Parallel Line"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "If a cat 🐱 looks up at a bird at 20° elevation, the bird looking down at the cat sees a ___ degree angle of depression.", "options": {"A": "70°", "B": "20°", "C": "160°", "D": "110°"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "To measure the height of a cloud ☁️, we use?", "options": {"A": "Angle of Depression", "B": "Angle of Elevation", "C": "Interior Angle", "D": "Reflex Angle"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "A person at the top of a lighthouse 🚨 looks at a ship. The angle measured is?", "options": {"A": "Elevation", "B": "Depression", "C": "Alternate", "D": "Corresponding"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "The angle of elevation from point A to B is 25°. What is the angle of depression from B to A? 🔄", "options": {"A": "155°", "B": "65°", "C": "25°", "D": "115°"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "Which instrument is commonly used to measure these angles? 📐", "options": {"A": "Compass", "B": "Protractor", "C": "Sextant", "D": "Clinometer"}, "correct_answer": "D"},
    {"id": 13, "difficulty": "easy", "question": "If the line of sight is ABOVE the horizontal, it's angle of?", "options": {"A": "Depression 😔", "B": "Elevation ⬆️", "C": "Rotation", "D": "Deflection"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "The horizontal line is drawn at the level of the observer's?", "options": {"A": "Foot 👣", "B": "Eye 👁️", "C": "Head", "D": "Shoulder"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "A watchman 👀 looks DOWN at a thief. Which angle is formed?", "options": {"A": "Elevation", "B": "Depression", "C": "Right Angle", "D": "Straight Angle"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "The angles of elevation/depression are always measured from the?", "options": {"A": "Vertical Line", "B": "Line of Sight", "C": "Object", "D": "Horizontal Line"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "From a cliff, looking at a boat 🚤, the angle is 15° below horizontal. This is angle of?", "options": {"A": "Elevation", "B": "Depression", "C": "Incidence", "D": "Reflection"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "If the angle of depression is 10°, it is a very ___ angle.", "options": {"A": "Large", "B": "Small", "C": "Obtuse", "D": "Reflex"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Can an angle of elevation be more than 90°? 🤔", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Only at night"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "A hot air balloon 🎈 is spotted. To find its height, we need its angle of?", "options": {"A": "Depression", "B": "Elevation", "C": "Descent", "D": "Ascent"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "A tower is 30m high. A man 1.5m tall observes the top at 30° elevation. How far is he from the tower? 🗼👨", "options": {"A": "49.28 m", "B": "28.5 m", "C": "52.5 m", "D": "30√3 m"}, "correct_answer": "A"},
    {"id": 22,  "difficulty": "medium", "question": "From a cliff 80m high, the angle of depression of a boat is 30°. How far is the boat from the cliff? ⛰️🚤", "options": {"A": "40 m", "B": "80√3 m", "C": "80/√3 m", "D": "138.56 m"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "The length of the shadow of a pole 🌲 is √3 times its height. The sun's elevation is?", "options": {"A": "45°", "B": "30°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "A 12m ladder 🪜 rests against a wall making 60° with ground. How high is its top?", "options": {"A": "6 m", "B": "6√3 m", "C": "12√3 m", "D": "10 m"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Two poles are 20m apart. From mid-point, their tops have elevations 30° & 60°. Find height difference. 📏", "options": {"A": "20/√3 m", "B": "20√3 m", "C": "10√3 m", "D": "40/√3 m"}, "correct_answer": "D"},
    {"id": 26, "difficulty": "medium", "question": "A kite string 🔴 is 100m long, inclined at 60° to ground. Kite's height? (Ignore sag)", "options": {"A": "50 m", "B": "50√3 m", "C": "100/√3 m", "D": "100 m"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "From a plane ✈️ at 1km height, depression of a ship is 45°. Distance of ship?", "options": {"A": "500 m", "B": "1 km", "C": "1.414 km", "D": "2 km"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "A man sees top of a building at 45°. Walking 20m closer, elevation becomes 60°. Building height? 🏢", "options": {"A": "10(√3+1) m", "B": "20(√3+1) m", "C": "10(3+√3) m", "D": "47.32 m"}, "correct_answer": "D"},
    {"id": 29, "difficulty": "medium", "question": "A cloud ☁️ is above a lake. From a point, its reflection has depression 45°, cloud's elevation is 30°. Cloud height above lake? (point 75m above lake)", "options": {"A": "75 m", "B": "150 m", "C": "75√3 m", "D": "300 m"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "From a 10m building 🏠, top of a cable tower has elevation 60° & bottom has depression 45°. Tower height?", "options": {"A": "10(√3+1) m", "B": "10√3 m", "C": "10(√3-1) m", "D": "20 m"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "The angle of elevation of sun ☀️ changes from 30° to 45°. Shadow of pole shortens by 20m. Pole height?", "options": {"A": "10(√3+1) m", "B": "20√3 m", "C": "10(3+√3) m", "D": "27.32 m"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "A man 2m tall sees top of a 50m tower at 45°. Distance from tower? 👨🗼", "options": {"A": "48 m", "B": "50 m", "C": "52 m", "D": "48√2 m"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "From a light house 🚨 100m high, depression of 2 ships are 45° & 30°. Distance between ships (on same side)?", "options": {"A": "100(√3-1) m", "B": "100√3 m", "C": "100(√3+1) m", "D": "200 m"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Top of a 20m tower & a 40m tower are in line with depression 30° from 60m tower. Distance between first two towers? 🗼🗼", "options": {"A": "20√3 m", "B": "40√3 m", "C": "60√3 m", "D": "80√3 m"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "A balloon 🎈 rising vertically is observed from 100m away. After 10s, elevation changes 30° to 60°. Speed? (m/s)", "options": {"A": "10/√3", "B": "20/√3", "C": "200/√3", "D": "15/√3"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "From a point on ground, top of a transmission tower has elevation 60°. 10m higher up, elevation is 45°. Tower height? 📡", "options": {"A": "5(√3+1) m", "B": "10(√3+1) m", "C": "5(3+√3) m", "D": "23.66 m"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "A statue 🗿 on a pillar subtends equal angles (15°) at two points 30m apart on ground towards pillar. Pillar height?", "options": {"A": "15√3 m", "B": "30 m", "C": "15(2+√3) m", "D": "40 m"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "A person flying a kite 🪁 lets out 150m string. Elevation is 60°. Another person sees it at 30° elevation. Vertical height difference between them?", "options": {"A": "75√3 m", "B": "150 m", "C": "50√3 m", "D": "100 m"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "A window is 12m above ground. Ladder's foot is 5m from wall. Ladder's angle of elevation? 🪟🪜", "options": {"A": "sin⁻¹(12/13)", "B": "tan⁻¹(12/5)", "C": "cos⁻¹(5/13)", "D": "tan⁻¹(5/12)"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "A pole is broken by wind 🌬️. Top touches ground 10m from foot, making 30° with ground. Original height?", "options": {"A": "10√3 m", "B": "20√3 m", "C": "10/√3 m", "D": "15 m"}, "correct_answer": "A"},

    {"id": 41, "difficulty": "hard", "question": "From top of a hill ⛰️, angles of depression of consecutive km stones on road are 30° & 45°. Hill height?", "options": {"A": "1/(√3-1) km", "B": "(√3+1)/2 km", "C": "1.366 km", "D": "2 km"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "hard", "question": "A man on cliff observes a boat at 30° depression. After 2 mins, depression is 60°. If boat moves towards cliff at 3 m/s, cliff height? ⏱️🚤", "options": {"A": "180√3 m", "B": "360√3 m", "C": "540 m", "D": "1080/√3 m"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "Two towers of heights 40m & 30m. Line joining tops makes 45° with horizontal. Distance between towers? 🗼🗼", "options": {"A": "10 m", "B": "20 m", "C": "30 m", "D": "40 m"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "A vertical pole & a tower are on same ground. From pole's top, depression of tower's foot is 60° & from tower's top, depression of pole's foot is 30°. If pole is 20m, tower height? 🚩🗼", "options": {"A": "60 m", "B": "80 m", "C": "40√3 m", "D": "90 m"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "From a point between two buildings 🏠🏢, their tops have elevations α & β. If heights are h1 & h2 and point is at distance d from first, find d in terms of h1, h2, α, β.", "options": {"A": "(h1 cot α)/(h2 cot β)", "B": "(h2 tan β - h1 tan α)/(tan α - tan β)", "C": "(h1 - h2)/(cot α - cot β)", "D": "(h1 cot β - h2 cot α)/(cot α - cot β)"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "hard", "question": "A person observes a bank robbery 👺 at 30° depression from a 50m building. Robber runs at 10m/s. After 5s, depression is 60°. Distance of robber from building initially?", "options": {"A": "50√3 m", "B": "100√3 m", "C": "150 m", "D": "75√3 m"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "A balloon moves vertically upwards from point P. After 1 min, elevation from P is 30°, after another minute it's 60°. Uniform speed of balloon? 🎈⬆️", "options": {"A": "h(√3-1) m/min", "B": "P dependent", "C": "constant", "D": "Can't find"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "hard", "question": "From a window (h m high) of a house, angles of elevation & depression of top & bottom of a lamp post are α & β. Lamp post height? 💡", "options": {"A": "h(tan α + tan β)", "B": "h(cot α + cot β)", "C": "h(tan α tan β)/(tan α + tan β)", "D": "h(tan α + tan β)/tan β"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "hard", "question": "Two vertical poles are 60m apart. Their tops make angles of elevation 30° & 60° from midpoint of line joining feet. Height ratio? 📐", "options": {"A": "1:3", "B": "3:1", "C": "√3:1", "D": "1:√3"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "The angle of elevation of a jet fighter ✈️ from point A on ground is 60°. After 10s, angle becomes 30°. If jet is flying at 720 km/hr, height?", "options": {"A": "1000√3 m", "B": "2000/√3 m", "C": "500√3 m", "D": "1500 m"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "A tower stands vertically on a bank of a river. From opposite bank, angle of elevation is 60°. Move 40m away, elevation becomes 30°. River width? 🌊🗼", "options": {"A": "20 m", "B": "40 m", "C": "60 m", "D": "80 m"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "A man on top of a tower observes a car at 45° depression. Car approaches tower, after 6s depression is 60°. If speed is 54 km/hr, tower height? 🚗🗼", "options": {"A": "135(√3-1) m", "B": "45(3+√3) m", "C": "90√3 m", "D": "135/(√3+1) m"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "Two ships ⚓ are observed from top of a 150m cliff. Their angles of depression are 60° & 45°. If ships are on same side, distance between ships?", "options": {"A": "150(√3-1) m", "B": "50(3-√3) m", "C": "150(1-1/√3) m", "D": "63.4 m"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "hard", "question": "A 1.5m tall man 👨 observes a bird on tree at 45°. Walks 10m towards tree, elevation becomes 60°. Bird height from ground?", "options": {"A": "5(3+√3) m", "B": "1.5+5(3+√3) m", "C": "10(√3+1) m", "D": "23.66 m"}, "correct_answer": "D"},
    {"id": 55, "difficulty": "hard", "question": "A vertical tower's top from a point 20m away is 45°. A flagstaff on top subtends 15° at same point. Flagstaff height? 🚩🗼", "options": {"A": "20(√3-1) m", "B": "20(2-√3) m", "C": "20(√3+1) m", "D": "40(√3-1) m"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "From an airplane ✈️, angles of depression of two boats in line are 45° & 30°. If height is 3000m, distance between boats?", "options": {"A": "3000(√3-1) m", "B": "3000(√3+1) m", "C": "3000 m", "D": "6000 m"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "A pole stands inside a circular park 🎡. From point on circumference, elevation of top is 30°. Walk 10√3m along circumference, elevation is 60°. Pole height?", "options": {"A": "5 m", "B": "10 m", "C": "15 m", "D": "20 m"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "hard", "question": "The angles of elevation of a rocket 🚀 from two tracking stations 2km apart are 45° & 30°. Rocket height above line joining stations?", "options": {"A": "2/(√3+1) km", "B": "2/(√3-1) km", "C": "1 km", "D": "√3 km"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "hard", "question": "From a point on ground, top of a minar has elevation θ. Move a distance d towards minar, elevation becomes 45°. Move further d, elevation becomes 90°-θ. Height of minar? 🕌", "options": {"A": "d√2", "B": "d(tan θ + cot θ)", "C": "d√(tan θ)", "D": "d/(cot θ - tan θ)"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Two vertical poles are x & y meters high. Line joining tops makes angle α with horizontal. Distance between poles?", "options": {"A": "(y-x) tan α", "B": "(y-x) cot α", "C": "(y+x) cot α", "D": "(y-x) sin α"}, "correct_answer": "B"}
  ]
}