Question

the angle of elevation of a top of a tower at a distance of 120 metre from a point a on the ground is 45 degree if the angle of elevation the top of the flagstaff fixed at the top of the tower at a is 60 degree then find the height of the flagstaff

Answer 1

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Answer 2

Answer: Height of the flagstaff is 87.84 m.

Step-by-step explanation:

Since we have given that

Distance from a point on the ground to the tower = 120 m

Angle of elevation of a top of a tower = 45°

Angle of elevation of a top of a flagstaff = 60°

So, as shown in the figure:

In ΔDBC,

$\tan 45^\circ=\frac{DB}{CB}\\\\1=\frac{DB}{120}\\\\DB=120\ m$

Similarly, in ΔABC,

$\tan 60^\circ=\frac{AB}{BC}\\\\\sqrt{3}=\frac{x+120}{120}\\\\120\times \sqrt{3}=x+120\\\\x=120\sqrt{3}-120\\\\x=120(\sqrt{3}-1)\\\\x=120\times (1.732-1)\\\\x=120\times 0.732\\\\x=87.84\ m$

Hence, Height of the flagstaff is 87.84 m.