12- At two points on the opposite sides of a pole the angles of elevation of the top of the pole are 30' and 45. If the height of the pole is 20m, find the distance between the two points.
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Class 10
>>Maths
>>Some Applications of Trigonometry
>>Heights and Distances
>>The angles of elevation of top of a pole
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The angles of elevation of top of a pole from two points Aand B on the horizontal line lying on opposite side of the pole are observed to be 30
0
and 60
0
If AB=100 m, then height of the pole is
Let the height of pole be PQ=h m.
And QB=d be the distance between B and foot of pole.
tan60
0
=
d
h
3
=
d
h
⇒d=
3
h
....(1)
tan30
0
=
100−d
h
3
1
=
100−d
h
⇒100−d=
3
h
Substitute the value of d from the equation (1), we get
⇒−
3
h
+100=
3
h
⇒100=h(
3
+
3
1
)
⇒100=h(
3
3+1
)
By doing cross multiplication
⇒100
3
=4h
⇒h=25
3
m