Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical
flag-staff of height 6 m. At a point on the plane, the angle of elevation of the
bottom and top of the flag-staff are 30° and 45° respectively. Find the height of
the tower. (Take 3 =1.73)​

Answer 1

Answer:

6√3 metres or 10.38 metres

Answer 2

Height of the tower is 8.22 m.

Step-by-step explanation:

Length of the flag staff = 6m

Let the height of the tower = h m

Angle of elevation of the top and bottom from a point D is 45° and 30° respectively.

From ΔACD,

tan45° = $\frac{AC}{CD}$

1 = $\frac{h+6}{CD}$

CD = (h + 6) ---------(1)

From ΔBCD,

tan30° = $\frac{h}{CD}$

$\frac{1}{\sqrt{3} }=\frac{h}{CD}$

CD = $h\sqrt{3}$ -------(2)

From equations (1) and (2),

h + 6 = h√3

h(√3 - 1) = 6

h = $\frac{6}{\sqrt{3}-1}$

  = $\frac{6}{1.73-1}$

  = 8.2191 m

  ≈ 8.22 m

Therefore, height of the tower is 8.22 m.

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