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 / 1
x = 191.3
Therefore, the distance from the car to the foot of the tower is 191.3 meters
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