Question

Q. A ladder 9m long reaches a point 9m below the top of a vertical flag staff. From the foot of the ladder the elevation of the top of the flagstaff is 60degrees. Find the height of the flag staff.

Answer 1

Answer:

Flag Staff length = 16.785 m

Step-by-step explanation:

Given: Length of Ladder, CD = 9 m

           Lenght of staff from top to foor of ladder , AD = 9 m

To find: Lenght of flag staff, AB

In Δ BCD,

Using Trignometric Ratio,

$sin\,60^{\circ}=\frac{BD}{CD}$

$\frac{\sqrt{3}}{2}=\frac{BD}{9}$

$BD=\frac{9\sqrt{3}}{2}$

$BD=\frac{15.57}{2}$    ( using value of √3 = 1.73 )

$BD=7.785$

⇒ AB = AD + DB

         = 9 + 7.785

         = 16.785 m

Therefore, Flag Staff length = 16.785 m

Answer 2

13.5m is the height of the flagstaff.

Step-by-step explanation:

As we know,

AD = CD = 9m

Therefore, triangle ACD is an isosceles Δ

∠CAB = 60°

∵ ∠CAD = ∠ACB = 30°

Thus, ∠BAD = 30°

In ΔABD,

sin 30°= BD/AD

⇒ BD = AD sin30° = 9 * 1/2 = 4.5

∵ BC = DC + BC = 9 + 4.5

= 13.5m

Thus, the height of the flagstaff is 13.5m.

Learn more: find the height

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