Question

FROM THE TOP OF A TOWER 50M HIGH THE ANGLES OF DEPRESSION OF THE TOP AND THE BOTTOM OF A POLE ARE OBSERVED TO BE 45DEGREE AND 60DEGREE RESPECTIVELY. FIND THE HEIGHT OF THE TOWER

Answer 1

Answer:150 root3

Step-by-step explanation:

150 root 3

Answer 2

Answer: The height of the tower is 21.13 m.

Step-by-step explanation:

Since we have given that

Height of the pole (H) = 50 m

Angle of depression of the top of the pole from the top of the tower = 45

Angle of depression of the bottom of the pole from the top of the tower = 60

As shown in the figure:

We need to find the height of the tower(h):

$H=\frac{h\cot x}{\cot x-\cot y}\\\\50=\frac{h\cot 45^\circ}{\cot 45^\circ-\cot 60^\circ}\\\\50=\frac{h}{1-\frac{1}{\sqrt{3}}}\\\\50=\frac{h\sqrt{3}}{\sqrt{3}-1}\\\\h=\frac{50(\sqrt{3}-1}{\sqrt{3}})\\\\h=21.13\ m$

Hence, the height of the tower is 21.13 m.