On a horizontal plane there is a vertical tower

Asked by admin @ 16/08/2021 in Math viewed by 340 People

On a horizontal plane there is vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60° and 30° respectively. Find the height of the tower and the flag pole mounted on it.

Answered by admin @ 16/08/2021

Answer:

The height of the tower is 3√3 m & the height of the flag mounted on it is 6√3 m .

Step-by-step explanation:

Let the height of the flag-pole (AD) be x & height of tower (AB) be h .

Angle of elevation 9 m away from the foot of the tower to the top of the flag-pole , ∠BCD = 60° & angle of elevation to the bottom of the flag-pole , ∠ACB = 30°

Let BC = 9 m

In right triangle , ∆ABC,

tan 30° = P/B = AB/BC

1/√3 = h/9

√3 h = 9

h = 9/√3

h = (9 ×√3) /(√3 × √3)

[On Rationalising]

h = 9√3/3

h = 3√3

Height of the tower ,h = 3√3 m ……….(1)

In right triangle , ∆DBC,

tan 60° = P/H = DB/BC

tan 60° = (AD + AB)/BC

√3 = (h + x)/9

9√3 = (h + x)

9√3 = 3√3 + x

[From eq 1]

9√3 - 3√3 = x

x = 6√3

Height of the flag mounted on it = 6√3 m

Hence, the height of the tower is 3√3 m & the height of the flag mounted on it is 6√3 m .

HOPE THIS ANSWER WILL HELP YOU…

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