Some Applications of Trigonometry Important Questions A straight highway leads to the foot of a tower. A man standing Read More » From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of 20m high building are 45∘ and 60∘ respectively. Find the height of the transmission tower. Read More » 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 tower from the foot of the building is 60°. If the tower is 50 m high, then find the height of the building. Read More » 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° respectively. If the bridge is at a height of 3 m from the banks, then find the width of the river. Read More » Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in 14th century. The lake has many Chhatris. One of them is shown below: Observe the picture. From a point A, h m above from water level, the angle of elevation of top of Chhatri (point B) is 45 and angle of depression of its reflection in water (point C) is 60. If the height of Chhatri above water level is (approximately) 10 m, then: (a) draw a well-labelled figure based on the above information. (b) find the height (h) of the point A above water level (Use √3 = 1.73) Read More » 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 pillar. From a point on the road between the pillars, the angle of elevation of the higher pillar is 60°, whereas that of the other pillar is 30°. Find the position of the point between the pillars and the height of each pillar. (Use √3 = 1.73) Read More » 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 above the first point P, its angle of elevation is 30°. Find: (a) The height of the tower. (b) The distance of the point P from the foot of the tower. (c) The distance of the point P from the top of the tower. Read More » Mr. Vinod is a pilot in Air India. During the Covid-19 pandemic, many Indian passengers were stuck at Dubai Airport. The government of India sent special aircraft to take them. Mr. Vinod was leading this operation. Read More » A hot air balloon is rising vertically from a point A on the ground which is at distance of 100m from a car parked at a point P on the ground. Amar, who is riding the balloon, observes that it took him 15 seconds to reach a point B which he estimated to be equal to the horizontal distance of his starting point from the car parked at P. Read More » A boy is standing on the top of light house. He observed that boat P and boat Q are approaching the light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. Read More » One evening, Kaushik was in a park. Children were playing cricket. Birds were singing on a nearby tree of height 80m. He observed a bird on the tree at an angle of elevation of 45°. When a sixer was hit, a ball flew through the tree frightening the bird to fly away. Read More » One observer estimates the angle of elevation to the basket of a hot air balloon to be 60°, while another observer 100 m away estimates the angle of elevation to be 30°. Find : (a) The height of the basket from the ground. (b) The distance of the basket from the first observer’s eye. (c) The horizontal distance of the second observer from the basket. Read More » From the top of a 7m high building, the angle of elevation of the top of a cable tower is 60 and the angle of depression of its foot is 30. Read More » 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 Read More » From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angle of depression 300 and 450 respectively. Read More » The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 600 and the angle of elevation Read More » From a point on the ground, the angle of elevation of the bottom and top of a transmission tower fixed at the top of 30m high building are 30° and 60° respectively. Read More » 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 one ship is exactly behind the other Read More » The angle of elevation of the top of a tower from a point on the ground which is 30 m away from the foot of the tower, is 30°. Find the height of the tower. Read More » 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 sun. Read More » An aeroplane when flying at a height of 3000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes Read More » 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 distance of 4 m, Read More » A spherical balloon of radius r subtends an angle of 60° at the eye of an observer. If the angle of elevation of its centre is 45° from the same point, Read More » 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 elevation of the top of second tower Read More »

From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of 20m high building are 45∘ and 60∘ respectively. Find the height of the transmission tower. Read More »

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 tower from the foot of the building is 60°. If the tower is 50 m high, then find the height of the building. Read More »

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° respectively. If the bridge is at a height of 3 m from the banks, then find the width of the river. Read More »

Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in 14th century. The lake has many Chhatris. One of them is shown below: Observe the picture. From a point A, h m above from water level, the angle of elevation of top of Chhatri (point B) is 45 and angle of depression of its reflection in water (point C) is 60. If the height of Chhatri above water level is (approximately) 10 m, then: (a) draw a well-labelled figure based on the above information. (b) find the height (h) of the point A above water level (Use √3 = 1.73) Read More »

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 pillar. From a point on the road between the pillars, the angle of elevation of the higher pillar is 60°, whereas that of the other pillar is 30°. Find the position of the point between the pillars and the height of each pillar. (Use √3 = 1.73) Read More »

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 above the first point P, its angle of elevation is 30°. Find: (a) The height of the tower. (b) The distance of the point P from the foot of the tower. (c) The distance of the point P from the top of the tower. Read More »

Mr. Vinod is a pilot in Air India. During the Covid-19 pandemic, many Indian passengers were stuck at Dubai Airport. The government of India sent special aircraft to take them. Mr. Vinod was leading this operation. Read More »

A hot air balloon is rising vertically from a point A on the ground which is at distance of 100m from a car parked at a point P on the ground. Amar, who is riding the balloon, observes that it took him 15 seconds to reach a point B which he estimated to be equal to the horizontal distance of his starting point from the car parked at P. Read More »

A boy is standing on the top of light house. He observed that boat P and boat Q are approaching the light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. Read More »

One evening, Kaushik was in a park. Children were playing cricket. Birds were singing on a nearby tree of height 80m. He observed a bird on the tree at an angle of elevation of 45°. When a sixer was hit, a ball flew through the tree frightening the bird to fly away. Read More »

One observer estimates the angle of elevation to the basket of a hot air balloon to be 60°, while another observer 100 m away estimates the angle of elevation to be 30°. Find : (a) The height of the basket from the ground. (b) The distance of the basket from the first observer’s eye. (c) The horizontal distance of the second observer from the basket. Read More »

From the top of a 7m high building, the angle of elevation of the top of a cable tower is 60 and the angle of depression of its foot is 30. Read More »

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 Read More »

From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angle of depression 300 and 450 respectively. Read More »

The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 600 and the angle of elevation Read More »

From a point on the ground, the angle of elevation of the bottom and top of a transmission tower fixed at the top of 30m high building are 30° and 60° respectively. Read More »

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 one ship is exactly behind the other Read More »

The angle of elevation of the top of a tower from a point on the ground which is 30 m away from the foot of the tower, is 30°. Find the height of the tower. Read More »

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 sun. Read More »

An aeroplane when flying at a height of 3000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes Read More »

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 distance of 4 m, Read More »

A spherical balloon of radius r subtends an angle of 60° at the eye of an observer. If the angle of elevation of its centre is 45° from the same point, Read More »

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 elevation of the top of second tower Read More »