height and distance
ASSIGNMENT –HEIGHT AND DISTANCE
1. An electric pole is ten metres high . If its shadow is 10square root3 m in length , find the elevation of the sun.[ Ans 30 degree]
2. The angle of elevation of the top of a tower , from a point on the ground and at a distance of 150m from its foot, is 30 degree . find the height of the tower correct to one decimal place .[ Ans 86.6m]
3.From a point P on the level ground, the angle of the elevation of the top of the tower is30 degree if the tower is high, how far is P from the foot of tower?[ans 173.2m]
4.A kite is flying at a height of 75 metres from the level of ground, attached to a string inclined of 60 degree to the horizontal. Find a length of the string to the nearest metre.[ans 86.6m]
5.if the length of the shadow cast by a pole be square root 3 times the length of the pole , find the angle of elevation of the sun[ans 30 degree].
6.Averticle tower is 20m high . A man at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is 2/3 . How far is he standing from the foot of the tower?[ans 17.92m]
7.The angle of elevation of a jet plane from appoint A on the ground is 60 degree . After a flight of 15 seconds , the angle of elevation changes to 30 degree . If the jet plane flying at a constant height of 1500square root 3 m ,find the speed of the jet plane .
[ans720 km/hr]
8 Determine the height of a mountain if the elevation of its top at an unknown distance from the base is 45 degree and at a distance 10 km further off from the mountain, along the same line, the angle of elevation is 30 degree. [Use tan 30 degree = 0.5774]{ans 13.66km}
9. The angle of elevation of the top of a rock from the top and the foot of a 100 m high tower are 30 degree and 45 degree respectively. Find the height of the rock[ans236.6m].
10. A man on the deck of a ship is 16 m above water level. He observes that the angle of elevation of the top of a cliff is 45 degree and the angle depression of the base is 30 degree. Calculate the distance of a cliff from the ship and the height of the cliff.[ans 27.712m,43.712m]
11. From the top a cliff 50 m high, the angle of depression of the top and the bottom of a tower are observed to be 30 degree and 45 degree respectively. Find the height of the tower.[ans 21.13m]
12. An aeroplane,when 3000 m high, passes vertically above another aeroplane at an instant when the angle of elevation of the two aeroplanes from the same point on the ground are 60 degree and 45 degree respectively. Find the vertical distance between the
aeroplanes at the instant [ans 1268m].
13. The angle of elevation of the top of a hill at the foot of a tower is 60 degree and the angle of elevation of the top of the tower from the foot of the hill is 30 degree. If the tower is 50 m high, what is the height of the hill.[ans 150m]
14. A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60 degree and the of depression of the point A from the top of the tower is 45 degree. Find the height of the tower.[ans 6.83m]
15. As observed from the top of a 150 m tall lighthouse, the angle of two ships approaching it are 30 degree and 45 degree. If one ship is directly behind the other, find the distance between the two ships.[ans 109.8m]
16. A tower is 50 m high. Its shadow is x m shorter when the sun’s attitude is 45 degree than when it is 30 degree. Find x correct to the nearest cm .[ans3660cm]
17. A 7 metres long flagstaff is fixed on the top of a tower on the horizontal plane. From a point of on the ground, the angles of elevation of the top and bottom of the flagstaff are 60 degree and 45 degree respectively. Find the height of the tower correct to the one place of decimal.[ans 9.56m]
18. From the top of a building 100m high, the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree. Find the height of the tower and its distance on the ground from the building.[ans 273.2m,100m]
19. A tree is broken by wind. The top stuck the ground at an angle of 30 degree and at a distance of 30 metres from the root. Find the whole height of the tree.[ans 51.96m]
20. The angle of elevation of a cloud from a point 60 m above the lake is 30 degree and the angle of depression of the reflection of the cloud in the lake is 60 degree. Find the height of the cloud.[ans 200m]
BY ANJALI
1. An electric pole is ten metres high . If its shadow is 10square root3 m in length , find the elevation of the sun.[ Ans 30 degree]
2. The angle of elevation of the top of a tower , from a point on the ground and at a distance of 150m from its foot, is 30 degree . find the height of the tower correct to one decimal place .[ Ans 86.6m]
3.From a point P on the level ground, the angle of the elevation of the top of the tower is30 degree if the tower is high, how far is P from the foot of tower?[ans 173.2m]
4.A kite is flying at a height of 75 metres from the level of ground, attached to a string inclined of 60 degree to the horizontal. Find a length of the string to the nearest metre.[ans 86.6m]
5.if the length of the shadow cast by a pole be square root 3 times the length of the pole , find the angle of elevation of the sun[ans 30 degree].
6.Averticle tower is 20m high . A man at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is 2/3 . How far is he standing from the foot of the tower?[ans 17.92m]
7.The angle of elevation of a jet plane from appoint A on the ground is 60 degree . After a flight of 15 seconds , the angle of elevation changes to 30 degree . If the jet plane flying at a constant height of 1500square root 3 m ,find the speed of the jet plane .
[ans720 km/hr]
8 Determine the height of a mountain if the elevation of its top at an unknown distance from the base is 45 degree and at a distance 10 km further off from the mountain, along the same line, the angle of elevation is 30 degree. [Use tan 30 degree = 0.5774]{ans 13.66km}
9. The angle of elevation of the top of a rock from the top and the foot of a 100 m high tower are 30 degree and 45 degree respectively. Find the height of the rock[ans236.6m].
10. A man on the deck of a ship is 16 m above water level. He observes that the angle of elevation of the top of a cliff is 45 degree and the angle depression of the base is 30 degree. Calculate the distance of a cliff from the ship and the height of the cliff.[ans 27.712m,43.712m]
11. From the top a cliff 50 m high, the angle of depression of the top and the bottom of a tower are observed to be 30 degree and 45 degree respectively. Find the height of the tower.[ans 21.13m]
12. An aeroplane,when 3000 m high, passes vertically above another aeroplane at an instant when the angle of elevation of the two aeroplanes from the same point on the ground are 60 degree and 45 degree respectively. Find the vertical distance between the
aeroplanes at the instant [ans 1268m].
13. The angle of elevation of the top of a hill at the foot of a tower is 60 degree and the angle of elevation of the top of the tower from the foot of the hill is 30 degree. If the tower is 50 m high, what is the height of the hill.[ans 150m]
14. A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60 degree and the of depression of the point A from the top of the tower is 45 degree. Find the height of the tower.[ans 6.83m]
15. As observed from the top of a 150 m tall lighthouse, the angle of two ships approaching it are 30 degree and 45 degree. If one ship is directly behind the other, find the distance between the two ships.[ans 109.8m]
16. A tower is 50 m high. Its shadow is x m shorter when the sun’s attitude is 45 degree than when it is 30 degree. Find x correct to the nearest cm .[ans3660cm]
17. A 7 metres long flagstaff is fixed on the top of a tower on the horizontal plane. From a point of on the ground, the angles of elevation of the top and bottom of the flagstaff are 60 degree and 45 degree respectively. Find the height of the tower correct to the one place of decimal.[ans 9.56m]
18. From the top of a building 100m high, the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree. Find the height of the tower and its distance on the ground from the building.[ans 273.2m,100m]
19. A tree is broken by wind. The top stuck the ground at an angle of 30 degree and at a distance of 30 metres from the root. Find the whole height of the tree.[ans 51.96m]
20. The angle of elevation of a cloud from a point 60 m above the lake is 30 degree and the angle of depression of the reflection of the cloud in the lake is 60 degree. Find the height of the cloud.[ans 200m]
BY ANJALI
