28. Height and Distance Solutions Part 1¶
The diagram is given below:
Let be the tower, the point of observation and as angle of elevation.
Since the tower is vertical it forms a right-angle triangle with right angle at . Thus,
.
The diagram is given below:
Let be the tower, the point of observation and the angle of elevation is .
Since the tower is vertical it forms a right-angle triangle with right angle at . Thus,
m.
The diagram is given below:
Let be the height of kite, be the length of string the angle of elevation is .
Since the kite would be vertical it forms a right-angle triangle with right angle at . Thus,
m.
The diagram is given below:
Let be the height of kite, be the length of string the angle of elevation is .
Since the kite would be vertical it forms a right-angle triangle with right angle at . Thus,
m.
The diagram is given below:
Let be the pole, the point where rope is tied to the ground and the angle of elevation is .
Since the pole is vertical it forms a right-angle triangle with right angle at . Thus,
m.
Thus, the acrobat has to climb m.
The diagram is given below:
Let be the pole, the point where rope is tied to the ground and the angle of elevation is .
Since the pole is vertical it forms a right-angle triangle with right angle at . Thus,
m.
The diagram is given below:
Let the shaded region represent the river and vertical lines the banks. represents the bridge, making an angle of with the bank. Let represent the width of river, which clearly makes a right angle triangle with right angle at .
Clearly, m.
Thus, width of the river is meters.
The diagram is given below:
Let be the observer, m tall. be the tower. Draw line parallel to which will make m. In right angle triangle angle of elevation . Given, m. Thus,
m. m.
The diagram is given below:
is the pole and is the ladder. is the point which the electrician need to reach to repair the pole which is m below the top of the pole. Total height of the pole is m, thus, m.
We are given than ladder makes an angle of with the horizontal.
m.
The diagram is given below:
![]()
is the point of observation. is the foot of the tower and is the top of the tower. is the height of the water tank above the tower. Given m .
In m, which is height of the toweer.
In m which is combined height of the tower and water tank. Thus, height or depth of the water tank m.
The diagram is given below:
![]()
The shaded region is the river. is the tree and is the initial point of the observer. is the final point of observation. Given, m. Let m and m.
In
In
m. m.
The diagram is given below:
![]()
is the tree before breaking. Portion has borken and has become which makes an angle of with remaining portion of tree standing. If m, then because original height of the tree is given as m.
In
The diagram is given below:
![]()
is the tree before breaking. Portion has borken and has become which makes an angle of with remaining portion of tree standing. If m, then where is the original height of the tree.
In
m.
The diagram is given below:
![]()
is the tower. Initial observation point is where angle of elevation is such that . is the second point of observation where angle of elevation is such that . Given, meters. Let be the height of the tower and be the distance of from the foot of the tower i.e. .
In
In meters.
The diagram is given below:
![]()
is the tower. When the sun’s altittude is the shadow reached . When the shadow reached the altitude of sun becomes . Let meters be the height and meters be the distance of of initial point of observation from foot of the tower. Given meters.
In
In meters.
The diagram is given below:
![]()
This problem is same as previous problem, where m is replaced by km. Processing similarly, we obtain km.
The diagram is given below:
![]()
This problem is same as two previous problems. The height of the mountain is km.
The diagram is given below:
![]()
This problem is same as -th. Proceeding similarly, we find width of river as m and height of the tree as m.
The diagram is given below:
![]()
Height of the plane is m which is . The ships are located at and . Let m and m.
In m.
In m.
The diagram is given below:
![]()
Let be the flag staff having height and be the shadow when sun’s altitude is . Let be the shadow when sun’s altitude is . If we let m then .
In .
In .
The diagram is given below:
![]()
Let be the height of the plane, equal to m. Let the shaded region present the river such that width m.
In m.
Clearly, m. In m.
The diagram is given below:
![]()
Let and represent the towers having height . Given the distance between towers is m which is . Let the point of observation be which is at distance from and from . Angle of elevations are given as and .
In .
In m.
The diagram is given below:
![]()
Let be the light house, and are the two locations of the ship. The height of the light house is given as m. The angle of elevations are given as and . Let m and m.
In .
In m.
The diagram is given below:
![]()
The diagram represents the top and as given in the problem. The angle of elevations are also given. Draw parallel to and thus, m. Let .
In m. Thus, m.
In m.
Height of toewr is
In m.
The diagram is given below:
![]()
Let and are the houses. Given m. Let the width of the street is m. The angle of depression and elevation are given as and respectively. Draw .
In m. Thus, is also m because is paralle to .
In m.
Thus, total height of the house m.
The diagram is given below:
![]()
Let represent the building and the tower. Let m and given m. Also, let m. Draw , thus m and m.
The angles of depression are given which would be same as angle of elevation from top and bottom of tower.
In m.
In m.
Height of the building m.
The diagram is given below:
![]()
Let represent the deck of the ship with height m and the hill. The water level is . Draw and let m.
The angle of elevation are shown as given in the question.
In m.
In m.
Thus, height of the hill m.
The diagram is given below:
![]()
Let be the line in which plane is flying and be the horizontal ground. Since the plane is flying at a constant height of m, we have m. Let m and m.
In m.
In m.
Thus, the plane flies m in s. Speed of plane km/hr.
The diagram is given below:
![]()
Let be the river and be the tree on the island in the river. Given wdith of the river as m. Let m m. The angles of elevation are shown as given in the question. Let m be the height of the tower.
In m.
In m.
The diagram is given below:
![]()
Let be the first tower and be the second tower. Given m and m. Let be the horizontal plane. Draw m and m. Angle of elevation is shown as given in the question from top of second tower to top of first tower to be .
In m.
Thus, total height of first tower is m.
The diagram is given below:
![]()
Let be the horizontal ground. Let and be the heights at which planes are flying. Given m. Also, given are angles of elevation of the two aeroplanes. Let point of observation be and m.
In m.
In m.
Therefore, distance between heights of two planes m.
The diagram is given below:
![]()
Let be the tower where is the foot of the toewr. Let be the point of observation. Given .
In m.
The diagram is given below:
![]()
Let be the wall and the ladder. Given distance of the foot of the ladder is m away from the wall i.e. m. The angle of elevation is given as .
In m.
The diagram is given below:
![]()
Let be the wall and the ladder. Given distance of the foot of the ladder is m away from the wall i.e. m. The angle of elevation is given as .
In m.
The diagram is given below:
![]()
Let be the electric pole, having a height of m. Let be the length of wire. The angle of elevation is given as .
In m.
The diagram is given below:
![]()
Let represent the height of kite. Given m. Let represent the length of the string. The angle of elevation is given as .
In m.
The diagram is given below:
![]()
Let represent the wall and the ladder. Given that the length of ladder is m. The angle of elevation of the wall from foot of the tower is given as .
In m.
The diagram is given below:
![]()
Let be the tower and be the flag staff, the heights of which are to be found. Let be the point of obsevation. Given that m. The angle of elevation of the foot and the top of flag staff are given as and i.e. and .
In m, which is height of the tower.
In m, which is combined height of tower and flag staff. Thus, m, which is height of flag staff.
This problem is same as 12. Put instead of .
The diagram is given below:
![]()
Let be the tower and the flag staff, whose height is m. Let be the point of observation. Given that angle of elevation of the foot of the flag staff is and that of top is i.e. and . Let m and m.
In m.
In m.
This problem is same as 15. Put m instead of m and instead of .
This problem is similar to 15. Put instead of and instead of .
The diagram is given below:
![]()
Let be the current height of the skydiver as m. and are two points observed at angle of depression and which woule be equal to angle of elevation from these points. Given that m. Let m.
In m.
In m.
m.
The diagram is given below:
![]()
Let be the tower having a height of m. Let and be the points observed such that and . Let m and m. We have to find .
In m.
In m.
The diagram is given below:
![]()
Let be the towerr having a height of m. Let and be the points observed such that and . Let m. Given m.
In m.
In m.
The diagram is given below:
![]()
Let be the towerr having a height of m. Let and be the points observed such that and . Let m. Given m.
In m.
In m.
Thus, m. Distance of initial point m.
The diagram is given below:
![]()
Let be the tower and be the building. Given m. is the horizontal plane joining foot of the building and foot of the tower having width m. Draw then m and m.
In m.
In m and m.
The diagram is given below:
![]()
Let be the tower and be the flag staff having heights and m respectively. The distance of foot of tower from the point of observation m. The angles of elevation of the foot and the top of the flag staff are and as given in the question.
In m.
In m.
The diagram is given below:
![]()
Let be the full tree and is the portion which has fallen. becomes after falling and angle of elevation is . Let the height of remaining portion of tree be m. Also, m.
In m.
Thus, total height of the tree is m.
The diagram is given below:
![]()
Let be the building with height m. Let be the flag with height m. Also, let distance between and foot of the building as m. The angle of elevation of top of the building is and that of the flag is .
In m.
In m.