In this page trigonometry heights and distances we are going to see questions of application problems in the topic trigonometry.
There are two types of angles
Angle of elevation: If the object is above the horizontal level from the eye we have to lift up our head to view the object.In this process our eyes move though the angle.This angle is called angle of elevation. |
Angle of depression: If the object is below the horizontal level from the eye,we have to move downwards our head to see the object.In this process our eyes move though an angle.This angle i called the angle of depression. |
Trigonometry Worksheets |
Solution |
(1) The angle of elevation of the top of the building at a distance of 50m from its foot on a horizontal plane is found to be 60 degree. Find the height of the building. | |
(2) A ladder placed against a wall such that it reaches the top of the wall of height 6 m and the ladder is inclined at an angle of 60 degree. Find how far the ladder is from the foot of the wall. | |
(3) From the top of the tower 30m height a man is observing the base of a tree at an angle of depression measuring 30 degree. Find the distance between the tree and the tower. | |
(4) A man wants to determine the height of a light house. He measured the angle at A and found that tan A = 3/4. What was the height of the light house if A was 40m from the base? | |
(5) The angle of elevation of the top of the light house at a distance of 30 m from its foot on a horizontal plane is found to be 60 degree. Find the height of the light house. | |
(6) A man is standing on the top of a multistoryed building 45 m high is looking at two advertising pillars on the side whose angle of depression are 30 degree and 45 degree. What was the distance between two pillars. | |
(7) Two men are on the opposite sides of a building. They measure the angles of elevation of the top of the building as 30 degree and 60 degree respectively. If the height of the building is 150 m, find the distance between the men. | |
(8) The angle of elevation of a multistoreyed building from a point on the toad changes from 30 degree to 60 degree as one walks 120 m along the road towards the building,find the height of the building. | |
(9) A flag staff stands on the top of 6 m high tower. From a point on the floor the angle of elevation of the top of the flag staff is 60 degree and from the same point the angle of elevation of the top of the tower is 45 degree. Find the height of the flag staff. | |
(10) The angles of depression of the top and the bottom of a 12 m high building from the top of the tower are 45 degree and 60 degree respectively. Calculate the height of the tower | |
(11) A tower is 100√3 meters high. Find the angle of elevation of its top from a point 100 meters away from its foot.
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(12) A string of a kite is 100 meters long and it makes an angle of 60° with horizontal. Find the height of the kite,assuming that there is no slack in the string.trigonometry heights and distances |
trigonometry heights and distances |
(13) The angle of elevation of the top of a tower at a distance of
130 m from its foot on a horizontal plane is found to be 63°. Find the
height of the tower. |
trigonometry heights and distances |
(14) A ladder is leaning against a vertical wall makes an angle of
20° with the ground. The foot of the ladder is 3 m from the wall.Find
the length of ladder. | |
(15) A kite flying at a height of 65 m is attached to a string inclined at 31° to the horizontal. What is the length of string. | |
(16) The length of a string between a kite and a point on the ground
is 90 m. If the string is making an angle θ with the level ground such
that tan θ = 15/8, how high will the kite be? | |
(17) An aeroplane is observed to be approaching the airpoint. It is
at a distance of 12 km from the point of observation and makes an angle
of elevation of 50 degree. Find the height above the ground. | |
(18) A balloon is connected to a meteorological station by a cable of
length 200 m inclined at 60 degree . Find the height of the balloon
from the ground. Imagine that there is no slack in the cable. | |
(19) The shadow of a building is 81 m long when the angle of elevation of the sun is 30. Find the height of the building. | |
(20) The angle of elevation of a tower at a point is 45 degree. After
going 40 m towards the foot of the tower the angle of elevation of the
tower becomes 60 degree. Calculate the height of the tower. |
trigonometry heights and distances |
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