The angle of elevation from a window to the top of a flag is 60° and the angle of depression to the base of the flag is 30°. The horizontal distance of the window from the flag is 6 m. Then the height of the flag is

Question

The angle of elevation from a window to the top of a flag is 60° and the angle of depression to the base of the flag is 30°. The horizontal distance of the window from the flag is 6 m. Then the height of the flag is (A) 2 √3 meters (B) 4 √3 meters (C) 8 √3 meters (D) 16 √3 meters

Tardigrade Admin · Accepted Answer

Let AB = height of flag <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/6d3cc2be77e2118b0ec28d57c0d44afb-.png" /> In ÎBDC, tan 60° = (BD/CD) BD = 6√3 In Î ACD, tan 30° = (AD/CD) ⇒ AD = (6/√3) Height of flag = BD + AD = 6√3 + (6/√3) = 6√3 +2√3 = 8√3 m

Q. The angle of elevation from a window to the top of a flag is $6 0^{\circ}$ and the angle of depression to the base of the flag is $3 0^{\circ}$ . The horizontal distance of the window from the flag is 6 m. Then the height of the flag is

$23$ meters

$43$ meters

$83$ meters

$163$ meters

Let $A B =$ height of flag

In $Δ B D C$ ,
$t an 6 0^{\circ} = \frac{B D}{C D}$
$B D = 63$
In $Δ A C D$ ,
$t an 3 0^{\circ} = \frac{A D}{C D}$
$\Rightarrow A D = \frac{6}{3}$
Height of flag $= B D + A D = 63 + \frac{6}{3}$
$= 63 + 23 = 83 m$

Q. The angle of elevation from a window to the top of a flag is 60∘ and the angle of depression to the base of the flag is 30∘. The horizontal distance of the window from the flag is 6 m. Then the height of the flag is

23​ meters

43​ meters

83​ meters

163​ meters