**1. An electric pole is 10 meter high. if its shadow is 10√3 metres in length, so find out the elevation of the sun.**

**Solution:**

**2. The angle of elevation of the top of a tower from a point on the ground and at a distance of 150 m from its foot is 300 . Find out the height of the tower correct to one place of decimal.**

**Solution:**

**3. A ladder is placed against a wall such that it reaches the top of the wall. The foot of the ladder is 1.5 metres away from the wall and the ladder is inclined at an angle of 600 with the ground. Find out the height of the wall.**

**Solution:**

**4. What is the angle of elevation of the sun when the length of the shadow of a vertical pole is equal to its height.**

**Solution:**

**5. A river is 60 m wide. A tree of unknown height is on one bank. The angle of elevation of the top of the tree from the point exactly opposite to the foot of the tree on the other bank is 300 . Find out the height of the tree.**

**Solution:**

**6. From a point P on level ground, the angle of elevation of the top of a tower is 30° . If the tower is 100 m high, how much far is P from the foot of the tower?**

**Solution:**

**7. From the top of a cliff 92 m high, the angle of depression of a buoy is 20° . Find out to the nearest meter, the distance of the buoy from the foot of the cliff.**

**Solution:**

**8. A boy is flying a kite with a string of length 100 m. If the string is tight and the angle of elevation of the kite is 26° 32’, find out the height of the kite correct to one decimal place, (ignore the height of the boy).**

**Solution:**

**9. An electric pole is 10 m high. A steel wire tied to the top of the pole is affixed at a point on the ground to keep the pole upright. If the wire makes an angle of 450 with the horizontal through the foot of the pole, find out the length of the wire**

**Solution:**

**10. A bridge across a river makes an angle of 45° with the river bank. If the length of the bridge across the river is 200 meters ,Find out the breadth of the river.**

**Solution:**

**11. A vertical tower is 20 m high. A man standing at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is 0.53. Find out How far is he standing from the foot of the tower?**

**Solution:**

**12. The upper part of a tree broken by wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 38**

^{0}30’ at a point 6 m from the foot of the tree. Find out**(i) the height at which the tree is broken.**

**(ii) the original height of the tree correct to two decimal places.**

**Solution:**

**13. An observer 1.5 m tall is 20.5 meters away from a tower 22 meters high. Find out the angle of elevation of the top of the tower from the eye of the observer.**

**Solution:**

**14. (i) In the adjoining figure, the angle of elevation from a point P of the top of a tower QR, 50 m high is 600 and that of the tower PT from a point Q is 30° . Find out the height of the tower PT, correct to the nearest meter.**

**(ii) From a boat 30° meters away from a vertical cliff, the angles of elevation of the top and the foot of a vertical concrete pillar at the edge of the cliff are 55° 40’ and 54° 20’ respectively. Find out the height of the pillar correct to the nearest meter.**

**Solution:-**

**15. From a point P on the ground, the angle of elevation of the top of a 10 m tall building and a helicopter hovering over the top of the building are 30° and 60° respectively. Find out the height of the helicopter above the ground.**

**Solution:**

**16. An aeroplane when flying at a heigt of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find out the distance between the two planes at the instant.**

**Solution:**

**17. A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 600 ; when he retires 20 m from the bank, he finds the angle to be 300 . Find out the height of the tree and the breadth of the river.**

**Solution:**

**18.The shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 45° to 30° . Find out the height of the tower, correct to two decimal places.**

**Solution:**

**19. From the top of a hill, the angles of depression of two consecutive kilometer stones, due east are found to be 300 and 450 respectively. Find out the distance of two stones from the foot of the hill.**

**Solution:**

**20. A man observes the angles of elevation of the top of a building to be 30° . He walks towards it in a horizontal line through its base. On covering 60 m the angle of elevation changes to 60° . Find out the height of the building correct to the nearest decimal place.**

**Solution:**

**21. At a point on level ground, the angle of elevation of a vertical lower is found to be such that its tangent is 5/12. On walking 192 m towards the tower, the tangent of the angle is found to be ¾. Find out the height of the tower.**

**Solution:**

**22. In the figure, not drawn to scale, TF is a tower. The elevation of T from A is x° where tan x = 2/5 and AF = 200 m. The elevation of T from B, where AB = 80 m, is y° . Find out :**

**(i) the height of the tower TF.**

**(ii) the angle y, correct to the nearest degree**

**Solution:-**

**23. From the top of a church spire 96 m high, the angles of depression of two vehicles on a road, at the same level as the base of the spire and on the same side of it are x° and y° , where tan x° = ¼ and tan y° = 1/7. Find out the distance between the vehicles.**

**Solution:-**

**24. In the adjoining figure, not drawn to the scale, AB is a tower and two objects C and D are located on the ground, on the same side of AB. When observed from the top A of the tower, their angles of depression are 45° and 60° . Find the distance between the two objects. If the height of the tower is 300. Give your answer to the nearest meter.**

**Solution:**

**25. The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30° . If the height of the second tower is 60 m, find out the height of the first tower.**

**Solution:**

**26. As observed from the top of a 80 m tall light house, the angles of depression of two ships on the same side of the light house in horizontal line with its base are 300 and 400 respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.**

**Solution:**

**27. The angle of elevation of a pillar from a point A on the ground is 45° and from a point B diametrically opposite to A and on the other side of the pillar is 60° . Find out the height of the pillar, given that the distance between A and B is 15 m.**

**Solution:.**

**28. From two points A and B on the same side of a building, the angles of elevation of the top of the building are 30° and 60° respectively. If the height of the building is 10 m, find out the distance between A and B correct to two decimal places.**

**Solution:**

**29. (i) The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find out the distance between the two ships. Give your answer correct to the nearest whole number.**

**(ii) An aeroplane at an altitude of 250 m observes the angle of depression of two boats on the opposite banks of a river to be 450 and 600 respectively. Find out the width of the river. Write the answer correct to the nearest whole number.**

**Solution:-**

**30. From a tower 126 m high, the angles of depression of two rocks which are in a horizontal line through the base of the tower are 16° and 12° 20’. Find out the distance between the rocks if they are on**

**(i) the same side of the tower**

**(ii) the opposite sides of the tower.**

**Lets assume CD as the tower of height = 126 m**

**A and B are the two rocks on the same line**

**Angles of depression are 16° and 12° 20’**

**Solution:**

**31. A man 1.8 m high stands at a distance of 3.6 m from a lamp post and casts a shadow of 5.4 m on the ground. Find out the height of the lamp post.**

**Solution:**

**32. The angles of depression of the top and the bottom of an 8 m tall building from the top of a multistoreyed building are 300 and 450 respectively. Find out the height of tire multi-storeyed building and the distance between the two buildings, correct to two decimal places.**

**Solution:**

**33. A pole of height 5 m is fixed on the top of a tower. The angle of elevation of the top of the pole as observed from a point A on the ground is 60° and the angle of depression of the point A from the top of the tower is 45° . Find out the height of the tower. (Take √3 = 1.732)**

**Solution:**

**34. A vertical pole and a vertical tower are on the same level ground. From the top of the pole the angle of elevation of the top of the tower is 60° and the angle of depression of the foot of the tower is 30° . Find out the height of the tower if the height of the pole is 20 m.**

**Solution:**

**35. From the top of a building 20 m high, the angle of elevation of the top of a monument is 450 and the angle of depression of its foot is 15° . Find out the height of the monument.**

**Solution:**

**36. The angle of elevation of the top of an unfinished tower at a point distant 120 m from its base is 45° .find out How much higher must the tower be raised so that its angle of elevation at the same point may be 60° ?**

**Solution:**

**37. In the adjoining figure, the shadow of a vertical tower on the level ground increases by 10 m, when the altitude of the sun changes from 45° to 30° . Find out the height of the tower and give your answer, correct to 1/10 of a meter.**

**Solution:**

**38. An aircraft is flying at a constant height with a speed of 360 km/h. From a point on the ground, the angle of elevation of the aircraft at an instant was observed to be 45° . After 20 seconds, the angle of elevation was observed to be 30° . Find out the height at which the aircraft flying. (use √3 = 1.732)**

**Solution:**

**Chapter Test**

**1. The angle of elevation of the top of a tower from a point A (on the ground) is 30° . On walking 50 m towards the tower, the angle of elevation is found to be 60° . Find out**

**(i) the height of the tower (correct to one decimal place).**

**(ii) the distance of the tower from A.**

**Solution:**

**2. An aeroplane 3000 m high passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are 60° and 45° respectively. Find out the vertical distance between the two planes.**

**Solution:**

**3. A 7 m long flagstaff is fixed on the top of a tower. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are 45° and 36° respectively. Find out the height of the tower correct to one place of decimal.**

**Solution:**

**4. A boy 1.6 m tall is 20 m away from a tower and observes that the angle of elevation of the top of the tower is 60° . Find out the height of the tower.**

**Solution:**

**5. A boy 1.54 m tall can just see the sun over a wall 3.64 m high which is 2.1 m away from him. Find out the angle of elevation of the sun.**

**Solution:**

**6. In the adjoining figure, the angle of elevation of the top P of a vertical tower from a point X is 60° ; at a point Y, 40 m vertically above X, the angle of elevation is 45° . Find out**

**(i) the height of the tower PQ**

**(ii) the distance XQ**

**(Give your answer to the nearest meter).**

**Solution:**

**7. An aeroplane is flying horizontally 1 km above the ground is observed at an elevation of 60° . After 10 seconds, its elevation is observed to be 30° . Find out the speed of the aeroplane in km/hr.**

**Solution:**

**8. A man on the deck of a ship is 16 m above the water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30° . find out the distance of the cliff from the ship and the height of the cliff.**

**Solution:**

**9. There is a small island in between a river 100 meters wide. A tall tree stands on the island. P and Q are points directly opposite to each other on the two banks and in the line with the tree. If the angles of elevation of the top of the tree from P and Q are 30° and 45° respectively, find out the height of the tree.**

**Solution:**

**10. A man standing on the deck of the ship which is 20 m above the sea-level, observes the angle of elevation of a bird as 30° and the angle of depression of its reflection in the sea as 60° . Find out the height of the bird.**

**Solution:**