The horizontal distance between two towers is 60 m and the angle of depression of the top of the first tower as seen from the top of the second is 30°. If the height of the second tower be 150 m, then the height of the first tower is

Question

The horizontal distance between two towers is 60 m and the angle of depression of the top of the first tower as seen from the top of the second is 30°. If the height of the second tower be 150 m, then the height of the first tower is (A) 90 m  (B) (150 - 60 bar 3 ) m (C) (150 + 20 bar 3 ) m (D) None of these

Tardigrade Admin · Accepted Answer

In Δ ABC , tan 30° = (BC/AC) ⇒ (1/3) = (h - 150/60) ⇒ h - 150 = (60/3) ⇒ h = 150 + 20 bar3 m

Q. The horizontal distance between two towers is $60 m$ and the angle of depression of the top of the first tower as seen from the top of the second is $3 0^{\circ}$ . If the height of the second tower be $150 m$ , then the height of the first tower is

$90 m$

$(150 - 60 \overset{ˉ}{3}) m$

$(150 + 20 \overset{ˉ}{3}) m$

None of these

In $Δ A BC, tan 3 0^{\circ} = \frac{BC}{A C}$
$\Rightarrow \frac{1}{3} = \frac{h - 150}{60}$
$\Rightarrow h - 150 = \frac{60}{3}$
$\Rightarrow h = 150 + 20 \overset{ˉ}{3} m$

Q. The horizontal distance between two towers is 60m and the angle of depression of the top of the first tower as seen from the top of the second is 30∘. If the height of the second tower be 150m, then the height of the first tower is

90m

(150−603ˉ)m

(150+203ˉ)m