Question

From the top of a tower of $50m$ high, Neha observes the angle of depression of the top and the foot of another building to be ${45}^o$ and ${50}^o$ respectively. Find the height of the building.

Answer 1

Given the height of the tower as $50meters$

Let the height of building be $xmeters$

By using the concept of the alternative angle we can find the desired angle as shown in the picture

$\tan {45}^{\circ }=\frac{ED}{AD}$

Therefore $ED=AD$. (1)

Now

$\tan {50}^{\circ }=\frac{50}{BC}$

$BC=42.01$. (Because $\tan {50}^{\circ }=1.19$)

From equation (1) we get $AD=42.01$

Now we can see that $CD=x$

And $ED+CD=50$

Therefore

$CD=50-42.01$

$CD=7.98meters$

Therefore $x=CD=7.98metres$