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| ee From the top of a spire of height 80 ft, the angles of depression of two cars on a straight road at the same level as that of the base of the spire and on the same side of it are 30° and 46°. Calculate the the distance between the two cars. ee |
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ee A ladder with its foot on a horizontal flat surface rests against a wall. It makes an angle of 15° with the horizontal. The foot of the ladder is 13 ft from the base of the wall. Find the height of the point where the ladder touches the wall.
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| ee A telegraph pole is 70 m high. Its shadow is 192.307 m in length. Find the angle of elevation of the sun. ee |
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ee Simon stands at 140 m away from the base of a building of height 50.96 m. Find the angle of depression of Simon from the top of the building.
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ee The angle of elevation of a cloud observed from a point at a height 150 ft above the level of water in a lake is 18° . The angle of depression of its image in the lake from the same point is 31°. Find the height of the cloud above the lake.
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ee A balloon at a height of 20 meters from the ground level is attached to a string inclined at 17o to the horizontal. Find the length of the string to the nearest meter.
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ee The angle of elevation of the top of a tree is 35o from a point 22 ft away from the foot of the tree. Find the height of the tree rounded to the nearest feet.
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| ee The angle of elevation of the top of a dowel from a point on the ground is 54°. After walking 18 ft towards the dowel, the angle of elevation becomes 67°. What is the height of the dowel rounded to the nearest foot? ee |
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ee A 47 ft high tree standing vertically upwards is broken by the wind in such a way that its top just touches the ground and makes an angle of 39° with the ground. At what height from the ground did the tree break?
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| ee A jet when 3340 m high passes vertically above another jet at an instant when the angles of elevation of the two jets from the same point on the ground are 60° and 46° respectively. Find the vertical distance between the two jets to the nearest meter. ee |
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ee The angle of elevation of the top of a tower from a point on the ground is 60°. If the height of the tower is 124 m, then find the distance of the point from the foot of the tower.
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| ee A flagstaff stands on the top of a building. At a distance of 56 ft away from the foot of the building, the angle of elevation of the top of a flagstaff is 40° and the angle of elevation of the top of a building is 25°. Find the height of the flagstaff to the nearest feet. ee |
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| ee The angle of elevation of the top of a hill from the foot of a tower is 46° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the distance between the foot of the tower and the foot of the hill is 45 ft, then find the height of the tower and the height of the hill rounded to the nearest feet. ee |
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| ee A man on the deck of a ship is 15 ft above sea level. He observes that the angle of elevation of the top of a cliff is 70° and the angle of depression of its base at sea level is 50°. Find the height of the cliff and its distance from the ship. ee |
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| ee From a shipmast head 145 meters high, the angle of depression of a boat is observed to be 40°. Find the distance of the boat from the ship. ee |
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| ee A boy is standing on the ground and flying a kite with a string of length 220 ft at an angle of elevation of 40°. Another boy is standing on the roof of a 94 ft high building and is flying his kite at an angle of elevation of 75°. Both the boys are facing each other. What shall be the length of the string of the kite of the second boy so that the two kites would touch? ee |
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ee From the top of a building of height h meters in a street, the angles of elevation and depression of the top and the foot of another building on the opposite side of the street are θ° and φ° respectively. Find the height of the opposite building. [Given h = 100, φ = 25, and θ = 40.]
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ee From the top of a tower of height h meters the angle of depression of a red car is φ° and the angle of depression of a blue car which is on the opposite side of the tower is θ°. If the distance between the foot of the tower and the red car is y meters, then find the height of the tower and the distanc between the two cars.
Assume that the points of location of the cars and the foot of the tower are collinear. [Given y = 115, θ = 55° and φ = 40°.] ee |
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ee Two towers are constructed on a plot of land. The angle of depression of the top of the second tower when seen from the top of the first tower is 50°. If the height of the first tower is 120 ft and the height of the second tower is 68 ft, then find the horizontal distance between the two towers.
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| ee The angle of elevation of an unfinished tower from a point 110 m away from its base is 30°. How much higher the tower be raised so that its angle of elevation from the same point will be 46°? ee |
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| ee A photographer using a camera photographs a rare bird roosting on a high branch of a tree at an angle of elevation of φ°. The distance between the camera lens and the bird is l ft. In order to get a clear picture, the photographer moves closer to the base of the tree. The angle of elevation of the bird is now θ°. Find the new distance between the camera lens and the bird. [Given l = 215, φ = 40° and θ = 75°.] ee |
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ee A flagpole of 8 m length is installed on the top of an office building 27 m high. The building and the pole subtend equal angles at a point outside the building which is at a height of 35 m. What is the distance of this point from the top of the pole?
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| ee The angle of elevation of the top of a cliff from the point Q on the ground is 30°. On moving a distance of 20 m towards the foot of the cliff the angle of elevation increases to φ°. If the height of the cliff is 17.3 m, then find φ. ee |
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| ee Tom and Sam are on the opposite sides of a tower of 140 meters height. They measure the angle of elevation of the top of the tower as 46° and 60° respectively. Find the distance between Tom and Sam. ee |
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| ee Two trees of equal height stand on either side of a roadway, which is 35 ft wide. At a point on the roadway between the trees, the elevations of the tops of the trees are 35° and 20°. Find the height of the trees. ee |
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| ee A man on the deck of a ship is 14 ft above water level. He observes that the angle of elevation of the top of a cliff is 60° and the angle of depression of the base is 40°. Find the distance of the cliff from the ship and the height of the cliff if the base of the cliff is at sea level. ee |
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