29. Height and Distance Solutions Part 2¶
The diagram is given below:
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Let be the lamp post having height m, and be the girl having height m. The distance of the grl from the lamp post is m. is the langeth of the shadow given as m. In the and is common, so third angle will be also equal. This makes the triangles similar.
m.
The diagram is given below:
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Let be the building having a height of m. Let and point of observations where angles of elevation are and respectively. Let be the line of foot of the building and foot of the observer which is a horizontal line. Let and are the heights of the observer. Draw so that m. Thus, m. We have to find .
In m.
In m.
Thus, m, which is the distance walked by the observer.
The diagram is given below:
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Let the height of the tower is m. When the altitude of the sun is let the length of the shadown be m. Then according to question length of shadow when the sun’s altitude i the length of shadow will be m longer i.e. .
In m.
In m and m.
The diagram is given below:
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Let be the building with m height. Let the height of tower be m represented by in the figure. Let be the point of observation at a distance from the foot of the building .
In m.
In m.
The diagram is given below:
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Let be the building having a height of m. Let be the multistoried building having height m. Foot of both the buildings are joined on horizontal plane i.e. . Draw a line parallel to which is . So is equal to which we have let as m. Clearly, m. Let height of to be m.
In .
In m.
The diagram is given below:
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Let be the pedestal having height m and be the statue having height m on top of pedestal. Let be the point of observation from where the angles of elevation as given in the question are and .
In .
In m.
This problem is similar to 55 and has been left as an exercise.
The diagram is given below:
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Let be the tower having height m. Let and be the position of two ships and angles of elevation are as given in the question. Let foor of the tower be in line with ships such that m and distance between the ships as m.
In m.
In m.
The diagram is given below:
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Let be the building and be thw tower having height m. The angles of elevation are shown as given in the question. Let distance between the foot of the tower and the building be m and height of the building be m.
In .
In m.
The diagram is given below:
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Let represent the banks of river and the bridge. Given that height of the bridge is m. m. The angles of depression from point is shown as given in the question. We have to find i.e. width of the river.
In m.
In m.
Thus, width of river m
The diagram is given below:
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Let and be the poles, both having the same height m. Let be the road having a width of m. Also, let be the point of observation from which angles of observation are shown as given in the question. Let m and thus m.
In m.
In m.
Since the poles have equal height, therefore m.
m.
The diagram is given below:
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Let be the tree having height m, the width of river. Let and be the foot of the poles on opposite banks of the river such that foot of the poles and the tree are in the same horizontal plane. Let and m. The angles of depression are shown as given in the question.
In m.
In m.
Thus, m.
The diagram is given below:
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Let be the tower having height m, be the flag staff having height m. Also, let point of observation at having angles of observation as and as given in the question such that m.
In .
In m.
The diagram is given below:
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Let and be the length of shadows with angles of depression and respectively such that m. Also let as the tower having height m and as the length of shadow with angle of depression having length m.
In m.
In m.