Question

The horizontal distance between two towers is $60\text{m}$ and the angle of depression of the top of the first tower as seen from the top of the second is ${30}^o$. If the height of the second tower be $150\text{m}$, then the height of the first tower is

• A. $(150+60\sqrt{3})\text{m}$
• B. $(150-60\sqrt{3})\text{m}$
• C. $(150+20\sqrt{3})\text{m}$
• D. None of these

Answer 1

The correct option is B $(150-60\sqrt{3})\text{m}$

As the Angle of Depression is given from the top of Second Tower

Hence, Second Tower is Larger than the First,so we can clearly see that, Height of First Tower must be less than the Height of the Second Tower $(=150m)$

We can see that, $BCDE$ is a Rectangle

so, $BC=ED=60$

$BE=CD=h\left(Let\right)$

Now, in $△AED$

$\tan {60}^o=\frac{AE}{ED}\Rightarrow \sqrt{3}=\frac{AE}{60}\Rightarrow AE=60\sqrt{3}$

So, Height of First Tower is $h=BE=AB-AE=150-60\sqrt{3}$