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14. A boy is standing on the top of a tower, observed that the angle of depression of a car on the horizontal ground is 60". On descending 140 m vertically downwards from the top of the tower, the angle of depression of the car is found to be 45°
(i) Find the height of the tower. (Take √3=1.732).
(ii) How far is the car from the foot of the tower?​

14 A Boy Is Standing On The Top Of A Tower Observed That The Angle Of Depression Of A Car On The Horizontal Ground Is 60 On Descending 140 M Vertically Downward class=

Sagot :

The height of the tower is 331.3 meters

The distance from the car to the foot of the tower is 191.3 meters

The situation forms a right angle triangle.

Right angle triangle:

Right angle triangle has one of its angles as 90 degrees. Therefore,

The height of the tower is the opposite side of the right angle triangle. The distance from the foot of the tower to the car is the adjacent side of the triangle formed.

Therefore, the following trigonometric can be formed from the relationship.

let

x = adjacent side = distance from the foot of the tower to the car.

Therefore,

[tex]x=\frac{140 + h}{tan60}=\frac{h}{tan45}[/tex]

cross multiply,

(140 + h)(tan 45) = h tan 60

140 tan 45 + h tan 45 = h tan 60

140 tan 45  =  h tan 60 -  h tan 45

140 = h√3 - h

140 = 1.732h - h

140 = 0.732h

h = 140 / 0.732

h = 191.256830601

h = 191.3

Therefore,

height of the tower = 140 + 191.3 = 331.3

The distance from the car to the foot of the tower is as follows;

  • x = 191.3 / tan 45

x = 191.3 / 1

x = 191.3

Therefore, the distance from the car to the foot of the tower is 191.3 meters

learn more on right triangle here; https://brainly.com/question/26750565?referrer=searchResults

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