# A light house is such that its angle of elevation from a point due north is $\theta$ and from a point due west is $\varphi$. Also the distance between the points is 'i' If the height of the lighthouse is  . Find k and n

Dear Student,

We form our diagram from given information , As :

Here height of light house  =  BD = ( Given ) and distance between both points  =  AC  = i

We know : tan

So, in triangle BCD we get

And in triangle ABD we get

And we apply Pythagoras theorem in triangle ABC and get

AC2  =  AB2 +  BC2  , Now we substitute values from equation 1 and 2 and as given distance between two points is " i " .

We can see that above equation only be satisfied is k = n = 1 .

Therefore ,

k = 1  and n = 1                                                                                    ( Ans )