The angles of elevation of the top of a tower from two points distant $s$ and $t$ from its foot are complementary. Then find the height of the tower.
Given: The angles of elevation of the top of a tower from two points distant $s$ and $t$ from its foot are complementary.
To do: To find the height of the tower.
Solution:
Let complementary angles be $\alpha$ and $90^o−\alpha$
$tan\alpha =\frac{h}{s}\ .....\ ( i)$
$tan( 90^o−\alpha)=cot\alpha =\frac{h}{t}\ ....\ ( ii)$
Multiply $( i)$ and $( ii)$
$\Rightarrow tan\alpha.cot\alpha =\frac{h}{s}.\frac{h}{t}$
$\Rightarrow \frac{h^2}{st}=1$
$\Rightarrow h=\sqrt{st}$
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