A) \[b\text{ }tan\text{ }\alpha \text{ }cot\beta \]
B) \[~b\text{ }cot\text{ }\alpha \text{ }tan\text{ }\beta \]
C) \[b\text{ }tan\text{ }\alpha \text{ }tan\text{ }\beta \]
D) \[b\cot \alpha \cot \beta \]
Correct Answer: A
Solution :
Let the height of the tower be\[h.\] In \[\Delta ABC,\] \[\tan \alpha =\frac{h}{AB}\] \[\Rightarrow \] \[AB=h\cot \alpha \] ?(i) In \[\Delta ABD,\] \[\tan \beta =\frac{b}{AB}\] \[\Rightarrow \] \[AB=b\cot \beta \] ?(ii) From Eqs.(i) and (ii) \[h=\cot \alpha =b\cot \beta \] \[\Rightarrow \] \[h=b\tan \alpha \cot \beta \]You need to login to perform this action.
You will be redirected in
3 sec