Class 10 (All in one) – Some Application of TrigonometryContact Number: 8527521718Class 10 (All in one) – Some Application of TrigonometryContact Number: 8527521718A ramp for disabled people in a hospital have slope not more than 30°. If the height of the ramp be 1 m, then find the length of ramp.
If the length of the shadow of a tower is increasing, then the angle of elevation of the Sun is also increasing. Is it true? Justify your answer.
Find the height of a tree, if it casts a shadow 17 m long on the level of ground, when the angle of elevation of the Sun is 45°.
If the Sun’s angle of elevation is 60° and height of the pole is , then find the length of the shadow.
Find the length of the shadow on the ground of a pole of height 6 m when the angle of elevation of the Sun is such that . CBSE 2013
If the height and length of the shadow of a man are the same, then find the angle of elevation of the Sun.
The figure shows the observation of point C from point A. Find the angle of depression from A. CBSE 2013
A tower stand near an airport. The angle of elevation of the tower from a point on the ground is such that its tangent is , Find the height of the tower, if the distance of observer from the tower is 120 m.
The angle of elevation of the top of a building 150 m high, from a point on the ground is 45°. Find the distance of the point from foot of the building.
A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, then find the length of the ladder. CBSE 2016
A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then find the height of the wall. CBSE 2013
The angle of depression of car parked on the road from the top of a 150 m high tower is 30°. Find the distance of the car from the tower. CBSE 2014
A kite if flying at a height of 30 m from the ground. The length of string from the kite to the ground is 60 m. Assuming that there is no slack in the string, find the angle of elevation of the kite at the ground.
A circus artist is climbing from the ground along a rope stretched from the top of a vertical pole and tied at the ground. The height of the pole is 12 m and the angle made by the rope with ground level is 30°. Calculate the distance covered by the artist in climbing to the top of the pole.
The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with the horizontal, then find the length of the wire.
A window in a building is at a height of 10 m from the ground. The angle of depression of a point P on the ground from the window is 30°. The angle of elevation of the top of the building from the point P is 60°. Find the height of the building. CBSE 2007
A player sitting on the top of a tower of height 20 m observes the angle of depression of a ball lying on the ground as 60°. Find the distance between the foot of the tower and the ball.
An observer, 1.5 m tall, is 20.5 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer. NCERT Exemplar; CBSE 2012
If two towers of heights x m and y m subtend angles of 30° and 60° respectively at the centre of a line joining their feet, then find the ratio x : y. CBSE 2015
A peacock is sitting on the top of a tree. It observes a serpent on the ground making an angle of depression of 30°. The peacock catches the serpent in 12 s with the speed of 300 m/min. What is the height of the tree? CBSE 2015
A person standing on the bank of a river observes that the angle of elevation of the top of tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and the width of the river. [take, = 1.732] CBSE 2008
From the top of a hill, the angles of depression of two consecutive kilometre stones due East are found to be 30° and 45°. Find the height of the hill. CBSE 2015
The shadow of a tower is 30 m long, when the Sun's angle of elevation is 30°. What is the length of the shadow, when Sun's elevation is 60°?
Two ships are there in the sea on either side of a lighthouse in such away that the ships and the base of the lighthouse are in the same straight line. The angle of depression of two ships as observed from the top of the lighthouse are 60° and 45°.
If the height of the lighthouse is 200 m, then find the distance between the two ships. CBSE 2014
From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are 30° and 45°, respectively. Find
(i) how far the pole is from the bottom of the tower.
(ii) the height of the pole. [take, = 1.732] CBSE 2015
The angles of elevation and depression of the top and bottom of a lighthouse from the top of a 60 m high building are 30° and 60°, respectively. Find the difference between the heights of the lighthouse and building.
A man standing on the deck of a ship, which is 10 m above the water level. He observes the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. Calculate the distance of the hill from the ship and height of the hill. CBSE 2016
The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 s, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 2500 m, then find the average speed of the aeroplane. CBSE 2013
The shadow of a flag staff is three times as long as the shadow of the flag staff, when the Sun rays meet the ground at an angle of 60°. Find the angle between the Sun rays and the ground at the time of longer shadow.
An aeroplane, when flying at a height of 4000 m from the ground, passes vertically above another aeroplane at an instant when the angles of elevation of two planes from the same point on the ground are 60° and 45°, respectively. Find the vertical distance between the aeroplanes at that instant.
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 opposite to each other on two banks and. in line with the tree. If the angles of elevation of the top of the tree from P and Q are respectively 30° and 45°, then find are height of the tree. [take, = 1.732]
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point R, 40 m vertically above X, the angle of elevation of the top Q of tower is 45°. Find the height of the tower PQ and the distance PX. [take, = 1.732] CBSE 2016
The angles of elevation of the top of a tower from two points on the ground at a distance a m and b m from the base of the tower and in the same straight line are complementary. Prove that the height of the tower is m.
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are α and β, respectively. Prove that the height of the tower is .
A window of a house is h m above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. Prove that the height of the other house is h (1+ tan α cotβ) m.
The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 m towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.
The angle of elevation θ of the top of a lighthouse as seen by a person on the ground is such that tan θ = . When the person moves a distance of 240 m towards the lighthouse, the angle of elevation becomes φ, such that . Find the height of the 4 lighthouse. CBSE 2013
The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45°. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60°, then find the height of the flagstaff. (use, = 1.73) CBSE 2014
A balloon is connected to an electric pole. It is inclined at 60° to the horizontal by a cable of length 215 m. Determine the height of the balloon from the ground. Also, find the height of the balloon, if the angle of inclination is changed from 60° to 30°. CBSE 2015
A man in a boat rowing away from a lighthouse 100 m high takes 2 min to change the angle of elevation of the lighthouse from 60° to 45°. Find the speed of boat.
Two ships are sailing in the sea on the either side of the lighthouse. The angles of depression of two ships as observed from the top of the lighthouse are 60° and 45°, respectively. If the distance between the ships is m, then find the height of the lighthouse.
At the foot of mountain, the elevation of its summit is 45°. After ascending 1000 m towards to mountain up a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain.
A ladder leaning against a vertical wall at an inclination a to the horizontal. Its foot is pulled away from the wall through a distance p, so that its upper end slides a distance q down the wall and then the ladder makes an angle β to the horizontal. Show that .
Sunita is an electrician and she has to repair an electric fault on a pole of height 5 m. She needs to reach to a point on the pole 1.3 m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of 60° from the horizontal, would enable her to reach the required position ? Further, how far from the foot of the pole should she place the foot of the ladder ? What value is indicated from this question?
