Question

Two vertical lamposts of equal heights stand on a either side of a roadway 50 m wide between the lampposts. The elevations of tops of the lampposts from a poiint between the lampposts are 60 and 30. Find the height of each lamppost and position of this point

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Answer 1

this is the given ecplaination hope it helps you bro

Answer 2

Answer:

The height of each lamppost is 21.650 and position of this point is 12.5 m away from lamp AB

Step-by-step explanation:

Refer the attached figure

Lamposts = AB and ED

Since heights are same

So, AB = ED

Distance between them i.e. BD = 50 m

Let BC be x

So, CD = 50-x

In ΔABC

$tan \tehta = \frac{Perpendicular}{Base}$

$tan60^{\circ} = \frac{AB}{BC}$

$\sqrt{3}= \frac{AB}{x}$

$\sqrt{3}x=AB$  ---1

In ΔECD

$tan \tehta = \frac{Perpendicular}{Base}$

$tan30^{\circ} = \frac{ED}{CD}$

$\frac{1}{\sqrt{3}}= \frac{ED}{50-x}$

$\frac{1}{\sqrt{3}}(50-x)= ED$  ---2

Since ED =AB

So, equate 1 and 2

$\sqrt{3}x=\frac{1}{\sqrt{3}}(50-x)$  

$3x=(50-x)$  

$4x=50$  

$x=12.5$  

Substitute in 1

$\sqrt{3}(12.5)=AB$

$21.650=AB$

So, the height of each lamppost is 21.650 and position of this point is 12.5 m away from lamp AB