Heights and Distances Practice Test 1

Question : 30 of 40

Marks: +1, -0

The height of a tower is h and the angle of elevation of the top of the tower is α. On moving a distance

h/2

towards the tower, the angle of elevation becomes β. What is the value of cot α - cot β?

Solution:

In ΔABC,

\cotβ={BC}/{AB}=x/h

Also In ΔABC,

\cotα={BD}/{AB}={h/2+x}/h

Now,

\cotα-\cotβ={h/2+x}/h-x/h=1/2

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