Two persons A and B are on the same side of a tower (T). Ifthe angles of elevation of the top of the tower as observed by A and B are 40°and 55° respectively and line /AB/ is 6m. Find the height of the tower.

Height of the tower is 12.07 meter.

Step-by-step explanation:

Given:

Angle of elevation observed from A = 40°

Angle of elevation from point B = 55°

Distance from A to B = 6 m

Note :

As we move towards the tower the angle of elevation will increase.

Let the height of the tower be "h'' meter.

And the distance from B to the base of the tower be "x'' m.

Adjacent length for angle 55° is ''x'' m and adjacent length from point A that is angle 40° is "6+x" m.

And we know that:

⇒

So arranging them in tangent angles.

⇒        ...equation (i)

⇒    ...equation (ii)

Dividing both the equation.

⇒

⇒

⇒

⇒

⇒

⇒

⇒ m

Now using the value of 'x' in equation (i).

⇒  

⇒

⇒ m

Height of the tower is 12.07 meter.

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