A vertical pole fixed to the horizontal ground is divided in the ratio 3: 7 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18 m away from the base of the pole, then the height of the pole (in meters) is:

Question

A vertical pole fixed to the horizontal ground is divided in the ratio 3: 7 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18 m away from the base of the pole, then the height of the pole (in meters) is: (A) 12 √15 (B) 12 √10 (C) 8 √10 (D) 6 √10

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f4562254f15adbfbba132c26ae73323b-.png" /> Let height of pole =10 ℓ tan α=(3 ℓ/18)=(ℓ/6) tan 2 α=(10 ℓ/18) (2 tan α/1- tan 2 α)=(10 ℓ/18) use tan α=(ℓ/6) ⇒ ℓ=√(72/5) height of pole =10 ℓ=12 √10

Q. A vertical pole fixed to the horizontal ground is divided in the ratio $3 : 7$ by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground $18 m$ away from the base of the pole, then the height of the pole (in meters) is:

$1215$

$1210$

$810$

$610$

Let height of pole $= 10 ℓ$
$tan α = \frac{3 ℓ}{18} = \frac{ℓ}{6}$
$tan 2 α = \frac{10 ℓ}{18}$
$\frac{2 t a n α}{1 - t a n ^{2} α} = \frac{10 ℓ}{18}$
use $tan α = \frac{ℓ}{6}$
$\Rightarrow ℓ = \frac{72}{5}$
height of pole $= 10 ℓ = 1210$

Q. A vertical pole fixed to the horizontal ground is divided in the ratio 3:7 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18m away from the base of the pole, then the height of the pole (in meters) is:

1215​

1210​

810​

610​