Question

A tower of height ${}^{\prime }{h}^{\prime }$ standing vertically at the center of a square f side length ${}^{\prime }{a}^{\prime }$ subtends the same angle ${}^{\prime }{\theta }^{\prime }$ at all the corner points of the square. Then

• A. $2h^2=a^{2}ta{n}^2\theta$
• B. $a^2=2h^{2}ta{n}^2\theta$
• C. $a^2=2h^{2}co{t}^2\theta$
• D. $2a^2=h^{2}co{t}^2\theta$

Answer 1

The correct option is A $2h^2=a^{2}ta{n}^2\theta$

In $△EFC$

$\tan \theta =\frac{EF}{EC}=\frac{h}{\frac{a}{\sqrt{2}}}\Rightarrow \frac{a}{\sqrt{2}}\tan \theta =h\Rightarrow a\tan \theta =\sqrt{2}h$

Squaring both the sides

$\Rightarrow {2h}^2=a^2{\tan }^2\theta$