Question

two mens on either side of a pole observe its top at the angles of elevation 45° and 60° respectively and the distance between two men is 48 meters,find the height of the pole?​

Answer 1

maybe it's right most

Answer 2

Answer:

the height of the pole is $65.57m$.

Step-by-step explanation:

Given that :

The angle of elevation of first man $=45^0$

The angle of elevation of second man $=60^0$

The distance between the two men $=48m$

Let the distance between the first man and the pole be $BD$

Let $BD=x$

$tan45^0=\frac{H}{x}$ (H is the height)

We know that $tan45^0 =1$

$1=\frac{H}{x}$

$H=x$    -- Let this be (i)

$tan60^0=\frac{H}{x-48}$

We know that $tan60^0=\sqrt{3}$

$\sqrt{3}=\frac{H}{x-48}$

$\sqrt{3}x-48\sqrt{3} =H$   -- Let this be (ii)

Substitute the value from (i) to (ii)

We get :

$\sqrt{3}H-H=48\sqrt{3}$

Taking $H$ outside,

$H(\sqrt{3}-1)=48\sqrt{3}$

$H=\frac{48}{\sqrt{3}-1 } m$

$H=65.57m$

Hence the get the height of the pole as $65.57m$