A person standing on the bank of a river observes that the angle of elevation of the top of a tower on the…

Question

A person standing on the bank of a river observes that the angle of elevation of the top of a tower on the opposite bank is 60° . When he moves 30 m away from the bank, he finds the angle of elevation to be 30° . Find the height of the tower and width of the river. (Take √3 = 1.732 )

Accepted Answer

1 mark for correct figure
Let the height of tower BA be $h$ m
and the width of river BC be $x$ m
$\tan 60^\circ = \sqrt{3} = \frac{h}{x}$
$\Rightarrow h = \sqrt{3}x$ --- (i)
$\tan 30^\circ = \frac{1}{\sqrt{3}} = \frac{h}{30+ x}$
$\Rightarrow h\sqrt{3} = 30 + x$ --- (ii)
Solving (i) and (ii), we get
$x = 15$
and $h = 15\sqrt{3}=15 \times 1.732 = 25.98$ m
$\therefore$ Height of tower = 25.98 m and width of river = 15 m

A person standing on the bank of a river observes that the angle of elevation of the top of a tower on the opposite…

More from “Double Triangle”