SECTION B — Very Short Answer Type Questions [2 Marks Each]
- 2 Marks Q1. A tower stands vertically on the ground. From a point on the ground, which is $15\text{ m}$ away from the foot of the tower, the angle of elevation of the top of the tower is found to be $60^\circ$. Find the height of the tower.
- 2 Marks Q2. A electrical pole is $10\text{ m}$ high. A steel wire tied to the top of the pole is fixed at a point on the ground and makes an angle of $30^\circ$ with the horizontal ground. Find the length of the wire.
- 2 Marks Q3. An observer $1.5\text{ m}$ tall is $28.5\text{ m}$ away from a chimney. The angle of elevation of her eyes to the top of the chimney is $45^\circ$. What is the height of the chimney?
- 2 Marks Q4. A kite is flying at a height of $60\text{ m}$ 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 $60^\circ$. Find the length of the string, assuming that there is no slack in th e string
- 2 Marks Q5. A ladder $15\text{ m}$ long just reaches the top of a vertical wall. If the ladder makes an angle of $60^\circ$ with the wall, find the height of the wall.
- 2 Marks Q6. From a point $20\text{ m}$ away from the foot of a tower, the angle of elevation of the top of the tower is $30^\circ$. Find the height of the tower
- 2 Marks Q7. A tower $50\text{ m}$ high casts a shadow $50\sqrt{3}\text{ m}$ long on the ground. Find the angle of elevation of the sun.
- 2 Marks Q8. The shadow of a vertical tower on level ground is increased by $10\text{ m}$ when the altitude of the sun changes from $45^\circ$ to $30^\circ$. Find the height of the tower
- 2 Marks Q9. A person is climbing a $20\text{ m}$ long ladder, which is tightly stretched and tied to the top of a vertical pole. If the rope makes an angle of $30^\circ$ with the ground, find the height of the pole.
- 2 Marks Q10. The angle of depression of a car parked on the ground from the top of a $75\text{ m}$ high tower is $30^\circ$. Find the distance of the car from the base of the tower.
- 2 Marks Q11. A vertical pole casts a shadow of length $3\sqrt{3}\text{ m}$ on the ground when the sun’s elevation is $60^\circ$. Find the height of the pole.
- 2 Marks Q12. A circus artist is climbing a $20\text{ m}$ 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 the ground level is $30^\circ$.
- 2 Marks Q13. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $30^\circ$ with it. If the distance between the foot of the tree to the point where the top touches the ground is $8\text{ m}$, find the height of the tree.
- 2 Marks Q14. A ladder rests against a vertical wall at an inclination of $60^\circ$ to the ground. If the foot of the ladder is $2.5\text{ m}$ away from the wall, find the length of the ladder.
- 2 Marks Q15. A boy is standing at a distance of $48\text{ m}$ from a building and observes the top of the building at an angle of elevation of $30^\circ$. Find the height of the building
- 2 Marks Q16. The angle of elevation of the top of a tower from a point on the ground, which is $30\text{ m}$ away from the foot of the tower, is $30^\circ$. Find the height of the tower.
- 2 Marks Q17. A $1.2\text{ m}$ tall girl spots a balloon moving with the wind in a horizontal line at a height of $88.2\text{ m}$ from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60^\circ$. Find the distance traveled by the balloon from the starting point.
- 2 Marks Q18. An aeroplane flying horizontally $1000\text{ m}$ above the ground is observed at an elevation of $60^\circ$ from a point on the ground. Find the horizontal distance of the aeroplane from the observer.
- 2 Marks Q19. A tower stands on a horizontal plane and is surmounted by a flagstaff of height $5\text{ m}$. At a point on the plane, the angle of elevation of the bottom of the flagstaff is $30^\circ$ and that of the top of the flagstaff is $60^\circ$. Find the height of the tower.
- 2 Marks Q20. The angle of elevation of the top of a building from the foot of the tower is $30^\circ$ and the angle of elevation of the top of the tower from the foot of the building is $60^\circ$. If the tower is $50\text{ m}$ high, find the height of the building.
- 2 Marks Q21. A bridge across a river makes an angle of $45^\circ$ with the river bank. If the length of the bridge across the river is $150\text{ m}$, find the breadth of the river
- 2 Marks Q22. From the top of a $7\text{ m}$ high building, the angle of elevation of the top of a cable tower is $60^\circ$ and the angle of depression of its foot is $45^\circ$. Determine the height of the tower.
- 2 Marks Q23. As observed from the top of a $75\text{ m}$ high lighthouse from the sea level, the angles of depression of two ships are $30^\circ$ and $45^\circ$. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
- 2 Marks Q24. 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 of $30^\circ$, which is approaching the foot of the tower with a uniform speed. Six seconds lat er, the angle of depression of the car is found to be $60^\circ$. Find the time taken by the car to reach the foot of the tower from this poi nt.
- 2 Marks Q25. The angles of elevation of the top of a tower from two points at a distance of $4\text{ m}$ and $9\text{ m}$ from the base of the tower and in the same straight line with it are complementary. Prove that the height of the t ower is $6\text{ m}$.
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