A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a second point h metres above the first, the depression of the foot of the tower is 60°. The horizontal distance of the tower from the point is.

Question

A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a second point h metres above the first, the depression of the foot of the tower is 60°. The horizontal distance of the tower from the point is. (A) h cot 60° (B) h cot 30° (C)  (h /3) cot 60° (D)  (h /3) cot 30°

Tardigrade Admin · Accepted Answer

Let PQ = x metres denote the tower so that Δ PAQ = 30°. Let AB = h metres. ∴ Δ BQA = 60° Now, (h/AQ) = tan 60° = √3 ∴ AQ = (h/√3) = h cot 60°

Q. A tower subtends an angle of 30 $^{\circ}$ at a point on the same level as the foot of the tower. At a second point h metres above the first, the depression of the foot of the tower is 60 $^{\circ}$ . The horizontal distance of the tower from the point is.

$h$ cot 60 $^{\circ}$

$h$ cot 30 $^{\circ}$

$\frac{h}{3}$ cot $6 0^{\circ}$

$\frac{h}{3}$ cot $3 0^{\circ}$

Let PQ = $x$ metres denote the tower so that $Δ P A Q = 3 0^{\circ}$ . Let AB = $h$ metres. $∴ Δ BQ A = 6 0^{\circ}$
Now, $\frac{h}{A Q}$ = tan $6 0^{\circ} = 3$
$∴$ AQ = $\frac{h}{3} = h$ cot $6 0^{\circ}$

Q. A tower subtends an angle of 30∘ at a point on the same level as the foot of the tower. At a second point h metres above the first, the depression of the foot of the tower is 60∘. The horizontal distance of the tower from the point is.

h cot 60∘

h cot 30∘

3h​ cot 60∘

3h​ cot 30∘