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Question

If the angles of the elevation of a tower from two points distant a and b (a>b) from its foot and in the same straight line from it are 300 and 600, then the height of the tower is

A
a+b
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B
ab
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C
ab
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D
ab
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Solution

The correct option is B ab
Let AB be the height of the tower and B be its foot
AB=h
BD=b
BC=a
ADC=60o
ACB=30o
In ABC
tan30=ABBC
13=ha
h=a3.....(1)
In ADB
tan60=hb
3=h
h=b3.....(2)
Multiplying (1) and (2)
h2=a3×b3
h2=ab
h=ab

1103763_1200557_ans_3d0a04fa881b480da7fe0319b45afcc4.png

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