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Q.

From the top of a hill, the angles of depression of two consecutive kilometer stones due east are found to be 30oand 45o. Find the height of the hill.


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a

1.365km

b

1.5km

c

1.7km

d

1.1km  

answer is A.

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Detailed Solution

Given that,
Angles of depression = 30oand 45o
Question ImageWe have the formula,
tanθ=HeightDistance We have to find the height of the hill,
Considering the distance between the nearer kilometer stone and the hill be ' x' km.
Then the distance between the farther kilometer stone and the hill will be ' 1+x' km as both are on the same side of the hill.
In triangle APB,
 tan450=hx   1=hx   h=x       …..(1)
In triangle AQB,
 tan300=h1+x   13=h1+x   1+x=3h From equation (1),
 1+h=3h 1=3h-h h=13-1 h=1.365km     (3=1.732)
Thus, the height is 1.365km.
Therefore the correct option is 1.
 
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