Answer:
New angle of depression of the boat from the top of observation tower is 45°
Step-by-step explanation:
height of the tower is
[tex]240m[/tex]
The angle of depression of the boat coming towards the lighthouse and found it to be 30˚
i) The a labelled figure on the basis of given information and the distance the boat from the foot of the observation tower is as follows
in triangle ABC
angel ACB= Tan 30˚
Tan C =
[tex] \frac{ab}{bc} [/tex]
Tan 30˚=
[tex] \frac{240}{bc} [/tex]
=
[tex] \frac{1}{ \sqrt{3} } = \frac{240}{bc} [/tex]
BC=
[tex]240 \sqrt{3} [/tex]
ii)after 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(√3 -1) m.
Actual distance is =
[tex] = 24 \sqrt{3 } - 240 \sqrt{3} + 24 0| [/tex]
[tex] = 240[/tex]
From triangle ABC
Tan D
[tex] = \frac{ab}{bd} [/tex]
Tan D
[tex] = \frac{240}{240} \\ = 1[/tex]
{tan45°=1}
Tan D= Tan 1
D=1
New angle of depression of the boat from the top of observation tower is 45°