Question 1 :
A well of diameter 3 m is dug 14 m deep. The Earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Question 2 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b8f273b2305849799ca.jpg' /> In the above figure, the shape of a gilli, in the gilli-danda game, is a combination of

Question 3 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b90273b2305849799cb.jpg' /> In the above figure, plumbline (sahul) is the combination of

Question 4 :
E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Is ∆ ABE ~ ∆ CFB ?

Question 5 :
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles find out if $\frac{OA}{OC}$ =$\frac{OB}{OD}$ ?

Question 6 :
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.

Question 7 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c75273b230584979ae1.PNG' /> In the above fig, Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, how much string does she have out? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

Question 8 :
It is given that $\Delta$ABC ~ $\Delta$DFE, $\angle$A =30°, $\angle$C = 50°, AB = 5 cm, AC = 8 cm and DF= 7.5 cm. Then, which of the following is true?

Question 9 :
The Angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.

Question 10 :
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foof of the tower, is 30°. Find the height of the tower.

Question 11 :
Two poless of equal heights are standing opposite to each ofher on either side of the road, which is 80 m wide. From a point between them on the road, the Angles of elevation of the top of the poless are 60° and 30°, respectively. Find the distances of the point from the poless.

Question 12 :
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 yr, she prefers to have a slide whose top is at a height of 1.5 m and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m and inclined at an angle of 60° to the ground. What should be the length of the slides in each case?

Question 13 :
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 45°. If one ship is exactly behind the ofher on the same side of the lighthouse, then find the distance between the two ships.

Question 14 :
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

Question 15 :
A straight highway leads to the foof of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foof of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foof of the tower from this point.

Question 16 :
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Question 17 :
A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle 30° with it. The distance between the foof of the tree to the point, where the top touches the ground is 8 m. Find the height of the tree.

Question 18 :
Two poless of equal heights are standing opposite to each ofher on either side of the road, which is 80 m wide. From a point between them on the road, the Angles of elevation of the top of the poless are 60° and 30°, respectively. Find the height of the poless.

Question 19 :
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foof is 45°. Determine the height of the tower.

Question 20 :
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 high building are $45^\circ and 60^\circ$, respectively. Find the height of the tower.

Question 21 :
The angle of elevation of the top of a building from the foof of the tower is 30° and the angle of elevation of the top of the tower from the foof of building is 60°. If the tower is 50 m high, then find the height of the building.

Question 22 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a62273b230584979933.jpeg' /> In the above image, a 1.2 m tall girl spofs a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.

Question 23 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a60273b230584979931.jpeg' /> In the above image, a circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with ground level is 30°.

Question 24 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a61273b230584979932.jpeg' /> In the above image, a TV tower stands vertically on a bank of a canal. From a point on the ofher bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foof of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.

Question 25 :
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eye to the top of the building increases from 30° to 60° as he walks tonwards the building. Find the distance he walked tonwards the building.