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 .?

Question

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 .?

Answer

**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.

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