Some Applications of Trigonometry

CBSE Class 10 Mathematics · every board question from this chapter, 2022–2026

• The string of a flying kite is tied to a point on the ground. The length of the string between the kite and the point on the…2026
• If the length of the shadow of a tower is √3 times that of its height, then altitude of the Sun is:2026
• A car is moving away from the base of a 30 m high tower. The angle of elevation of the top of the tower from the car at an…2026
• From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower…2026
• A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as 60^°. If AB=5 √3 m, then…2026
• A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff. From a point on the ground 30 m away…2026
• The angle of elevation of the top of a building from a point A, on the ground, is 30°. On moving a distance of 24 m towards its…2026
• A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string…2026
• A boy standing on a horizontal plane is flying a kite with a string of length 60 m, at an angle of elevation of 30°. Another boy…2026
• Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an…2026
• Tejas is standing at the top of a building and observes a car at an angle of depression of 30° as it approaches the base of the…2026
• Radio towers are used for transmitting a range of communication services including radio and television. The tower will either…2026
• Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an…2026
• A 30 m long rope is tightly stretched and tied from the top of pole to the ground. If the rope makes an angle of 60° with the…2025
• A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is 10 √3 m away from…2025
• An observer 1.8 m tall stands away from a chimney at a distance of 38.2 m along the ground. The angle of elevation of top of…2025
• A kite is flying at a height of 150 m from the ground. It is attached to a string inclined at an angle of 30° to the horizontal.…2025
• Assertion: A ladder leaning against a wall, stands at a horizontal distance of 6 m from the wall. If the height of the wall up to…2025
• A 1.5 m tall boy is walking away from the base of a lamp post which is 12 m high, at the speed of 2.5 m/sec. Find the length of…2025
• Two ships are sailing in the sea on either side of a lighthouse. The angles of depression to the two ships as observed from the…2025
• The angle of elevation of an airborne helicopter from a point A on the ground is 45°. After a flight of 15 seconds, the angle of…2025
• A lighthouse stands tall on a cliff by the sea, watching over ships that pass by. One day a ship is seen approaching the shore…2025
• Passenger boarding stairs, sometimes referred to as boarding ramps, stair cars or aircraft steps, provide a mobile means to…2025
• Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and…2025
• A drone was used to facilitate movement of an ambulance on the straight highway to a point P on the ground where there was an…2025
• The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a 58 m high base. As part of the project,…2025
• From a point on the ground, which is 30 m away from the foot of a vertical tower, the angle of elevation of the top of the tower…2024
• The length of the shadow of a tower on the plane ground is √3 times the height of the tower. The angle of elevation of the Sun is:2024
• At some time of the day, the length of the shadow of a tower is equal to its height. Then, the Sun's altitude at that time is:2024
• The ratio of the length of a pole and its shadow on the ground is 1: √3. The angle of elevation of the Sun is:2024
• If a vertical pole of length 7 · 5 m casts a shadow 5 m long on the ground and at the same time, a tower casts a shadow 24 m…2024
• From the top of a 15 m high building, the angle of elevation of the top of a tower is found to be 30^°. From the bottom of the…2024
• Two pillars of equal lengths stand on either side of a road which is 100 m wide, exactly opposite to each other. At a point on…2024
• A man on a cliff observes a boat at an angle of depression of 30° which is approaching the shore to the point immediately beneath…2024
• The angle of elevation of an aircraft from a point A on the ground is 60°. After a flight of 30 seconds, the angle of elevation…2024
• A person standing on the bank of a river observes that the angle of elevation of the top of a tower on the opposite bank is 60^°.…2024
• From a point on a bridge across the river, the angles of depressions of the banks on opposite sides of the river are 30° and 60°…2024
• From the top of a building 60 m high, the angles of depression of the top and bottom of the vertical lamp post are observed to be…2024
• From the top of a 45 m high light house, the angles of depression of two ships, on the opposite side of it, are observed to be…2024
• From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m…2024
• From a window 15 metres high above the ground in a street, the angles of elevation and depression of the top and the foot of…2024
• The angles of depression of the top and the bottom of a 8 m tall building from the top of a multi-storeyed building are 30° and…2024
• The angles of depression of the top and the bottom of a 50 m high building from the top of a tower are 45° and 60°, respectively.…2024
• The angle of elevation of a jet plane from a point A on the ground is 60^°. After a flight of 30 seconds, the angle of elevation…2024
• A pole 6m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point P on the…2024
• If a pole 6 m high casts a shadow 2 √3 m long on the ground, then sun's elevation is:2023
• Find the length of the shadow on the ground of a pole of height 18 m when angle of elevation θ of the sun is such that tan θ=6/7.2023
• The length of the shadow of a tower on the plane ground is √3 times the height of the tower. Find the angle of elevation of the…2023
• A straight highway leads to the foot of a tower. A man standing on the top of the 75 m high tower observes two cars at angles of…2023
• A ladder set against a wall at an angle 45° to the ground. If the foot of the ladder is pulled away from the wall through a…2023
• One observer estimates the angle of elevation to the basket of a hot air balloon to be 60°, while another observer 100 m away…2023
• As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 60°. If…2023
• The angle of elevation of the top of a tower 24 m high from the foot of another tower in the same plane is 60^°. The angle of…2023
• The angle of elevation of the top of a vertical tower from a point P on the ground is 60^°. From another point Q, 10 m vertically…2023
• The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60^° and the angle of…2023
• An aeroplane when flying at a height of 3000 m from the ground passes vertically above another aeroplane at an instant when the…2023
• Two pillars are standing on either side of a 80 m wide road. Height of one pillar is 20 m more than the height of the other…2023
• Radio towers are used for transmitting a range of communication services including radio and television. The tower will either…2023
• Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a…2023
• Two boats are sailing in the sea 80 m apart from each other towards a cliff AB. The angles of depression of the boats from the…2022
• An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two banks of a river to be…2022
• A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with…2022
• In Fig. 3, AB is tower of height 50 m. A man standing on its top, observes two cars on the opposite sides of the tower with…2022
• From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°. If…2022
• The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the…2022
• Two men on either side of a cliff 75 m high observe the angles of elevation of the top of the cliff to be 30° and 60°. Find the…2022
• There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are points directly…2022
• An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the…2022
• The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds, the angle of elevation…2022
• From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60^° and the angle of depression of…2022
• The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^°. From a point Y, 40 m vertically…2022
• From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60^° and the angle of depression of…2022
• A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression…2022
• Case Study-1: Kite festival is celebrated in many countries at different times of the year. In India, every year 14^th January is…2022
• Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh…2022

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