1. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is
2. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?
a) 5.73 unit
b) 4 unit
c) 12 unit
d) Data Inadequate
3. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is
b) 13.8 m
c) 2.3 m
4. An observer 1.6 m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is
a) 22.72 m
b) 21.6 m
c) 23.4 m
d) 20.98 m
5. From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is
d) 86.5 m
6. The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:
7.A man is standing on the deck of a ship, which is 10m above water level. He observes the angle of elevation of the top of a light house as 600 and the angle of depression of the base of lighthouse as 300. Find the height of the light house.
8. From the top of a building 60m high, the angle of elevation and depression of the top and the foot of another building are α and β respectively. Find the height of the second building.
a) 60(1+ tan α tanβ)
b) 60(1+ cot α tanβ)
c) 60(1+ tan α cotβ)
d) 60(1- tan αcotβ)
9. From the top of a tower 75m high, the angles of depression of the top and bottom of a pole standing on the same plane as the tower are observed to be 300 and 450 respectively. Find the height of the pole.
10. A 10 m long flagstaff is fixed on the top of a tower on the horizontal plane. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are 600 and 450 respectively. Find the height of the tower.
a) 5(√3 + 1)m
b) 5(√3 + 3)m
c) 10(√3 - 1)m
d) 10(√3 + 1)m