Question : The angle of depression of a point situated at a distance of 70 m from the base of a tower is $60^{\circ}$. The height of the tower is:
Option 1: $35\sqrt{3}$ m
Option 2: $70{\sqrt3}$ m
Option 3: $\frac{70{\sqrt3}}{3}$ m
Option 4: $70$ m
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Correct Answer: $70{\sqrt3}$ m
Solution :
Length of the tower, $AB$ = $h$ m
$\angle DAC$ = $\angle ACB$ = $60^{\circ}$
$BC$ = 70 m
In $\triangle ABC$,
$\tan 60^{\circ}$ = $\frac{AB}{BC}$
$⇒\sqrt3=\frac{h}{70}$
$\therefore h=70\sqrt3$ m
Hence, the correct answer is $70\sqrt{3}$ m.
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