A man is between two tall buildings 8m away from the taller building. If the angle of the top of the building from where he stans bears N 8degrees W for the taller one and N
12degrees E for other. How far is he from the other building if the taller building is 6/5 as to the other
Hard to tell, but I am assuming that you meant to say that the taller building is 6/5 as far away as the shorter building.
If so, then the shorter building is 5/6 as far away, or 20/3 m.
Something tells me the heights matter, but I can't see how, from the data. The directions don't seem to enter in here anywhere.
To find the distance of the man from the other building, we can use trigonometry. Let's denote the distance between the man and the taller building as x.
First, let's understand the given information. The angle measured N 8 degrees W means that the angle made between the line joining the man and the taller building and the North direction is 8 degrees in the West direction. Similarly, the angle N 12 degrees E means that the angle made between the line joining the man and the other building and the North direction is 12 degrees in the East direction.
We can now create a diagram to better visualize the situation:
```
N
^
|
x | \
| 12°
| \
------|---------------------------> East-West direction
8m | /
| 8°
|
```
In this diagram, the taller building is to the left (West) of the man, and the other building is to the right (East) of the man.
Now, let's analyze the situation. We have a triangle formed between the man, the taller building, and the other building. The angle between the line connecting the man and the taller building and the line connecting the man and the other building is 8 degrees + 12 degrees = 20 degrees.
Since the taller building is 6/5 times the height of the other building, the ratio of their heights can be represented as (6/5)x : x, where x is the height of the other building.
Using trigonometry, we can set up the following equation:
tan(20 degrees) = (6/5)x / 8m
To solve for x, we can rearrange the equation and solve:
x = (8m * tan(20 degrees)) / (6/5)
Using a scientific calculator, we can calculate the value of tan(20 degrees), which is approximately 0.36397.
Plugging in the values:
x = (8m * 0.36397) / (6/5)
x = (8m * 0.36397) / 1.2
Evaluating the expression:
x ≈ 2.425m
Therefore, the man is approximately 2.425 meters away from the other building.