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An instrument was set up at point 200m away from a transmission tower.The angle of elevation to the top of the tower was 30� whereas the angle of depression to the bottom was 2�.Calculate the total height of the transmission tower A 122.454m B 115.470m C 108.486 m D 129.438 m .?
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An instrument was set up at point 200m away from a transmission tower....
**Solution:**
Let's assume the height of the transmission tower is 'h' meters.
**Angle of Elevation:**
The angle of elevation to the top of the tower is given as 30°. This means that the line of sight from the instrument to the top of the tower makes an angle of 30° with the horizontal line.
**Angle of Depression:**
The angle of depression to the bottom of the tower is given as 2°. This means that the line of sight from the instrument to the bottom of the tower makes an angle of 2° with the horizontal line.
We can draw a diagram to represent the situation as follows:
```
C
/|
/ |
/ |h
/ |
/ |
A /_____| B
200m
```
Using trigonometry, we can calculate the height of the transmission tower.
**Using Tangent Function:**
We can use the tangent function to find the height of the tower.
In triangle ABC, we have:
tangent(30°) = h/200
Solving for 'h', we get:
h = 200 * tangent(30°)
**Using Tangent Function:**
Similarly, in triangle ABC, we have:
tangent(2°) = h/200
Solving for 'h', we get:
h = 200 * tangent(2°)
**Calculating the Height of the Tower:**
To find the total height of the transmission tower, we need to add the heights calculated using both the angle of elevation and the angle of depression.
Total height = h (from angle of elevation) + h (from angle of depression)
Total height = 200 * tangent(30°) + 200 * tangent(2°)
Using a calculator, we can find the value of the total height.
Total height ≈ 122.454 meters
Therefore, the total height of the transmission tower is approximately 122.454 meters.
Hence, the correct option is A. 122.454m.
Let's assume the height of the transmission tower is 'h' meters.
**Angle of Elevation:**
The angle of elevation to the top of the tower is given as 30°. This means that the line of sight from the instrument to the top of the tower makes an angle of 30° with the horizontal line.
**Angle of Depression:**
The angle of depression to the bottom of the tower is given as 2°. This means that the line of sight from the instrument to the bottom of the tower makes an angle of 2° with the horizontal line.
We can draw a diagram to represent the situation as follows:
```
C
/|
/ |
/ |h
/ |
/ |
A /_____| B
200m
```
Using trigonometry, we can calculate the height of the transmission tower.
**Using Tangent Function:**
We can use the tangent function to find the height of the tower.
In triangle ABC, we have:
tangent(30°) = h/200
Solving for 'h', we get:
h = 200 * tangent(30°)
**Using Tangent Function:**
Similarly, in triangle ABC, we have:
tangent(2°) = h/200
Solving for 'h', we get:
h = 200 * tangent(2°)
**Calculating the Height of the Tower:**
To find the total height of the transmission tower, we need to add the heights calculated using both the angle of elevation and the angle of depression.
Total height = h (from angle of elevation) + h (from angle of depression)
Total height = 200 * tangent(30°) + 200 * tangent(2°)
Using a calculator, we can find the value of the total height.
Total height ≈ 122.454 meters
Therefore, the total height of the transmission tower is approximately 122.454 meters.
Hence, the correct option is A. 122.454m.
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An instrument was set up at point 200m away from a transmission tower.The angle of elevation to the top of the tower was 30� whereas the angle of depression to the bottom was 2�.Calculate the total height of the transmission tower A 122.454m B 115.470m C 108.486 m D 129.438 m .?
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An instrument was set up at point 200m away from a transmission tower.The angle of elevation to the top of the tower was 30� whereas the angle of depression to the bottom was 2�.Calculate the total height of the transmission tower A 122.454m B 115.470m C 108.486 m D 129.438 m .? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about An instrument was set up at point 200m away from a transmission tower.The angle of elevation to the top of the tower was 30� whereas the angle of depression to the bottom was 2�.Calculate the total height of the transmission tower A 122.454m B 115.470m C 108.486 m D 129.438 m .? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An instrument was set up at point 200m away from a transmission tower.The angle of elevation to the top of the tower was 30� whereas the angle of depression to the bottom was 2�.Calculate the total height of the transmission tower A 122.454m B 115.470m C 108.486 m D 129.438 m .?.
An instrument was set up at point 200m away from a transmission tower.The angle of elevation to the top of the tower was 30� whereas the angle of depression to the bottom was 2�.Calculate the total height of the transmission tower A 122.454m B 115.470m C 108.486 m D 129.438 m .? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about An instrument was set up at point 200m away from a transmission tower.The angle of elevation to the top of the tower was 30� whereas the angle of depression to the bottom was 2�.Calculate the total height of the transmission tower A 122.454m B 115.470m C 108.486 m D 129.438 m .? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An instrument was set up at point 200m away from a transmission tower.The angle of elevation to the top of the tower was 30� whereas the angle of depression to the bottom was 2�.Calculate the total height of the transmission tower A 122.454m B 115.470m C 108.486 m D 129.438 m .?.
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