a) The angle of elevation of the sun when the length of the shadow of a pole is equal to its height is 45°. T
b) If the ratio between the length of the shadow of a pole and its height is √3:1, then elevation of the sun is 30°. T
c) If the ratio between the length of the shadow of the tower and its height is 1:√3, 45°.
d) The numerical value of depression from the top of a tower of a point on the ground is same as elevation of the top from the point on the ground.
2) The angles of the elevation of the top of a tower from two points distant 150m and 100m from the foot of the tower and in the same straight line with it, are complementary. Prove that height of the tower is 50√6 m.
3) The shadow of a tower standing on a level ground is found to be 45m longer, when the sun's altitude is 30° than when it was 60°. Find the height of the tower. 38.94m
4) A tower is 100√3m high. Find the angle of elevation of its top from a point 100m away from its foot. 60°
5) The angle of elevation of a tower at a point is 45°. After going 40 m towards the foot of the tower, the angle of elevation of the tower become 60°. Find the height of the tower. 94.64m
6) From the top of a hill, the angles of a depression of two consecutive kilometre stones due Easter are found to be 30° and 45°. Find the height of the hill. 1336m
7) A person observed the angle of elevation of the top of a tower as 30°. He walked 50m towards the foot of the tower along level ground and found the angle of elevation of the top of the tower as 60°. Find the height of the tower. 43.3m
8) The string of a kite is 100m long and it makes an angle of 60° with the horizontal. Find the height of the kite, assuming that there is no slack in the string. 86.6m
9) A parachute is descending vertically and makes an angle of elevation of 45° and 60° at 2 observing points 100m apart from each other on the left side of himself. Find the maximum height from which he falls and the distance of the point where he falls on the ground from the first observation point. 236.6m, 136.6m
10) On the same side of a tower, two objects are located observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150m, find the distance between the objects. 63.4m
11) The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sun rays meet the ground at an angle of 60°. Find the angle between the sun rays and the ground at the time of longer shadow. 30°
12) The shadow of a vertical tower on level ground increases by 10 m, when the altitude of the sun changes from angle of elevation 45° to 30°. Find the height of the tower. 13.66m
13) The pilot of helicopter, at an altitude of 1200m, finds that the two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60° and 45° respectively. Find the distance between the two shops. 507.2m
14) The angle of elevation of an aeroplane from A on the ground is 45°, after 15 seconds flight, the angle of elevation changes to 30°. If the aeroplane is flying at a height of 3000m, find the speed of the plane . 146.6 m/sec
15) The angle of elevation of a jet fighter from a point P on the ground is 60°. After 15 seconds flight the angle of elevation changes to 30°. If the jet is fying at a speed of 720 kmph , find the height at which jet is fying. 2598m
16) From the top of a cliff 100m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60° respectively . Find the height of the tower. 200/3
17) From the top of a building, 60m high, the angles of depression of the top and bottom of a vertical lamp post are observed to be 30° and 60°respectively. Find
a) the horizontal distance between the building and the lamp post. 34.64m
b) the difference between the heights of the building and the lamp-post. 20m
18) The horizontal distance between two trees of different heights is 60m. The angle of depression of the top of the first tree when seen from the top of the second tree is 45°. If the height of the second tree is 80 m. Find the height of the first tree. 20m
19) Two men are at opposite sides of a tower. The measure the angle of elevation of the top of the tower as 45° and 60° degree respectively. The height of the tower is 30m. Find the distance between the two men. 47.32m
20) Two points A and B are on opposite sides of a tower. The top of the tower makes angles of 30° and 45° at A and B respectively. If the height of tower is 40 m, find the distance AB. 109.28
21) A fire in building B is reported on telephone to two fire station P and Q, 10 km apart from each other on a straight road. P observes that the fire is at an angle of 60° to the road and Q observes that it is an angle of 45° to the road. Which station should send its team and how much will this team have to travel ? 1st team, travels 7.32km
22) Two men on either side of the cliff 80m high observes the angles of elevation of the top of the cliff to be 30° and 60°degree respectively. Find the distance between the two men. 184.8m
23) An aeroplane at an altitude of 200m observes the angles of depression of opposite points on the two banks of a river to be 45°and 60°. Find the width of the river. 315.4
24) Two boats approach a lighthouse in mid-sea from opposite directions . The angles of elevation of the top of the lighthouse from the two boats are 30°and 45° respectively. If the distance between the two boats is 100m, find the height of the lighthouse. 36.6
25) From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be p and q. If the height of the lighthouse be h metres and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is h(tan p + tan q)/(tan p tan q)
26) A flagstaff stands on the top of a 5m high tower from a point on the ground. The angle of elevation of the top of the flagstaff is 60° and from the same point the angle of elevation of the top is 45°. Find the height of the flagstaff . 3.66m
27) A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the flagstaff is 45°. Find the height of the tower . 9.562m
28) A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff . At a point on the plane 70m away from the tower, an observer notices that the angles of elevation of the top and bottom of the flagstaff are respectively 60° and 45°. Find the height of the flagstaff and that of the tower . 51.24m, 70m
29) A tree 12m height, is broken by the wind in such a way that its top touches the ground and makes an angle of 60° with the ground. At which height from the bottom the tree is by the wind? 5.568m
30) A tree is broken by the wind. The top struck the ground at an angle of 30° and at a distance of 30m from the root. Find the whole height of the tree. 51.96m
31) The upper part of a tree broken over by the wind makes an angle of 30° with the ground and the horizontal distance from the root of the tree of the point where the top of the thee meets the ground is 20m. Find the height of the tree before it was broken. 34.64m
32) An aeroplane 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 the speed of the aeroplane in kmph . 415.68 kmph
33) A man is standing on the deck of a ship, which is 8m above the water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill is 30°. Calculate the distance of the hill from the ship and the height of the hill. 1.856m, 32m
34) In the given figure ABCD is a rectangle in which segment AP and AQ are drawn as shown. Find the length of (AP + AQ). 180m
35) At the foot of a mountain, the elevation of its summit is 45° after ascending 1 km towards the mountain up an incline of 30°, the elevation changes to 60°. Find the height of the mountain. 1.366km
From the top of a tower 15 m high the angle of depression of the copper and the bottom of the polar observed to be 45 degree and 60° respectively find the height of the tangles of the elevation of the top of a tower from 2.0 B from the base and in the same side straight line with its complementary prove that the height of the tower is root 5 degrees found to 10 m longer than 60° find the height of the term angle of depression at a point on the level ground viewed from 20 m high in row and the top of the building at 30 degree and 45 calculate the height of the building opposite to each other road which is 100 m white from a point between them on the road angle of elevation of the tops of 30 and 60 i Bangalore elevation of the click from a fixed point of a distance of KM towards the top of the Cliff angle of it is found the angle of elevation show that the height of the clipping vertical tower stands in horizontal surmounted by aorticulture the point on the plane the angle the division of the plaster is and that are the top of prove that the height of the tower is aeroplane flying horizontally one km about the ground is observed at an elevation of 60 after 10 second it's television is observed with 30 find the speed of the aeroplane a man on the top of a tower stand on the seashore find the report coming towards in text 10 minutes from angle of depression to change from 30 to 60 also will the boat reach the seashore the angle of elevation of a Clive from a fixed point a is 45 after going after distance of 600 m toward the top of the clay inclination angle of elevation of a cloud from lake is and angle of depression of reflection the lake prove that the height of the cloud
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