Questions & Answers

Question

Answers

A. $$25\sqrt{2}$$

B. $$25\sqrt{3}$$

C. 25

D. 12.5

Answer

Verified

130.5k+ views

then $$\tan \theta =\dfrac{\text{Perpendicular} }{\text{Base} } =\dfrac{AB}{BC}$$........(1)

So let us draw the diagram,

Let us consider the height of the tower AB to be x meter.

And it is given that the distance between any point C to the foot of the tower AB is 25 m, i.e, BC = 25 m.

The angle of elevation from the point C to the top of the tower is $$45^{\circ}$$.

$$\therefore \angle C=45^{\circ }$$

Now for the right angle triangle $$\triangle ABC$$,

$$\tan \angle C=\dfrac{AB}{BC}$$ [by formula (1)]

$$\Rightarrow \tan 45^{\circ }=\dfrac{x}{25}$$

$$\Rightarrow 25\times \tan 45^{\circ }=x$$

$$\Rightarrow x=25\times \tan 45^{\circ }$$

Now as we know that the value of $$\tan 45^{\circ }$$ is 1.

So from the above equation we get,

$$ x=25\times 1$$

$$\Rightarrow x=25$$