C & D is an observation post on the same horizontal ground at the foot A of a vertical tower AB, the tower is 18cm due north and 24m east of C. the angle of elevation of B from D is equals to 35\deg .give the diagram illustration, cal. to 3 sig. fig. height AB, Distance CD, angle of elevation of B from C and bearing of C & D

Question

C & D is an observation post on the same horizontal ground at the foot A of a vertical tower AB, the tower is 18cm due north and 24m east of C. the angle of elevation of B from D is equals to 35\deg .give the diagram illustration, cal. to 3 sig. fig. height AB, Distance CD, angle of elevation of B from C and bearing of C & D

Answer 1

I put C at the origin, but where is D?

Answer 2

also, once D is located, you want the bearing of C & D -- from where?

Answer 3

To solve this problem, we will first create a diagram to visualize the situation.

Diagram:
```
B
|
|
|
C -------------- D
|
|
|
A
```

We can see that the observation post C is on the same horizontal ground as D, at the foot A of the vertical tower AB. The tower is 18 cm due north and 24 m east of C. The angle of elevation of B from D is 35 degrees.

Let's calculate the required values:

1. Height AB:
To find the height AB, we can use the tangent function. Given the angle of elevation of B from D (35 degrees), we can calculate the height AB using the following equation:
tan(35) = AB/CD

AB = CD * tan(35)

2. Distance CD:
Given that the tower is 18 cm due north and 24 m east of C, we can use Pythagoras' theorem to calculate the distance CD:
CD^2 = (24m)^2 + (18cm)^2

3. Angle of elevation of B from C:
To find the angle of elevation of B from C, we can use the inverse tangent function. We know the length of the opposite side (AB) and the adjacent side (CD). Using the following equation:
tan(angle) = opposite/adjacent

angle = atan(AB/CD)

4. Bearing of C & D:
The bearing of C & D is the angle between the line connecting C & D and the reference line (North). To calculate the bearing, we need to find the angle between the line CD and the North direction. To do this, we can find the angle between the line CD and the East direction (90 degrees) using the following equation:
tan(bearing) = opposite/adjacent

bearing = atan((24m)/(18cm)) + 90 degrees

Remember to convert the final answer to the required number of significant figures (3 significant figures in this case).

By following the steps above, you will be able to calculate the height AB, distance CD, angle of elevation of B from C, and the bearing of C & D.