Q1. 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°. The height of the tower is:
Q2. A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, the height of the wall is:
Q3. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower is:
Q4. If the height of a pole and the distance of a point from its foot are equal, the angle of elevation of the top of the pole is:
Q5. An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?
Solve on white paper.
Q6. 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, what is the length of the wire?
Q7. 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, find the width of the river.
Q8. The angle of elevation of the top of a building from the foot of a 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, find the height of the building.
Q9. 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 other on the same side of the lighthouse, find the distance between the two ships.
Q10. A 1.2 m tall girl spots 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 some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
Q11. Case Study:
A group of students of class X visited a lighthouse at the request of their teacher. The teacher said that the lighthouse is a tall tower with a bright light at the top, and it is used to guide ships and warn them of dangerous areas. From the top of the 100 m high lighthouse, they observe two ships on opposite sides of the lighthouse. The angles of depression to the ships are 30° and 45°.
(i) Draw a labelled figure on the basis of the given information.
(ii) Find the distance of the ship at 45° depression from the foot of the lighthouse.
(iii) Find the distance of the ship at 30° depression from the foot of the lighthouse.
(iv) What is the distance between the two ships?