Let A B and P Q be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q , which are feet of these two poles. Let π 8 and θ be the angles of elevation from C to P and A , respectively. If the height of pole P Q is twice the height of pole A B , then tan 2…

Question

Let A B and P Q be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q , which are feet of these two poles. Let &#960; 8 and &#952; be the angles of elevation from C to P and A , respectively. If the height of pole P Q is twice the height of pole A B , then tan 2 &#952; is equal to

Aicharya · Accepted Answer

From the given information in the question we can draw the following diagram

Let $B C = C Q = x & A B = h$ and $P Q = 2 h$

So $\tan θ = \frac{h}{x}$ and $\tan \frac{π}{8} = \frac{2 h}{x}$

$\Rightarrow \frac{\tan θ}{\tan (\frac{π}{8})} = \frac{1}{2}$

$\Rightarrow \tan θ = \frac{1}{2} (\sqrt{2} - 1)$

$\Rightarrow \tan^{2} θ = \frac{1}{4} (3 - 2 \sqrt{2})$

Let A B and P Q be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q ,…

Solution