from the top of a vertical mast 150m high,two huts on the same ground level are observed. One due east and the other due west of the mast. Their angles of depression are 60° and 45° respectively. Find the distance between the huts. Solutuons with diagram
plss draw the diagram I dnt get u
Are you lazy pls draw the diagram
The sketch please... 🙏🙏🙏
Pls, kindly sketch a diagram for better comprehension
Diagram,where is it
I didn't get the answer with my diagram
Please the diagram.
I assume you made the simple sketch and translated the angles of depression given to be the base angles of the two right-angled triangle.
Let the distance of the hut with the 60° angle be x, let the other distance be y
case1: tan60 = 150/x
x = 150/tan60
case 2: .....
y =
find x+y
To find the distance between the huts, we can use trigonometry and the given angles of depression.
Let's start by drawing a diagram to visualize the scenario.
```
H
|\
| \
60° | \ 45°
| \
|____\
M G
```
In the diagram:
- H represents the height of the mast (150m).
- M represents the top of the mast.
- G represents the ground level where the huts are located.
- The line MH represents the distance from the top of the mast to the hut in the east.
- The line MG represents the distance from the top of the mast to the hut in the west.
Using trigonometry, let's consider the right-angled triangle MHG to solve for the distance between the huts.
For triangle MHG:
1. Angle MHG = 90° (because it's a right-angled triangle)
2. Angle HGM = 60° (given angle of depression)
3. Angle HMG = 45° (given angle of depression)
Now, let's calculate the sides of the triangle using trigonometric ratios:
1. tan(HGM) = MG / HM
tan(60°) = MG / HM
√3 = MG / HM (since tan(60°) = √3)
2. tan(HMG) = MG / HG
tan(45°) = MG / HG
1 = MG / HG (since tan(45°) = 1)
Since HG = height of the mast = 150m, we can find MG using equation 2.
MG = 1 * HG
MG = 1 * 150m
MG = 150m
Now, let's find HM using equation 1.
√3 = MG / HM
√3 = 150m / HM (since MG = 150m)
HM = 150m / √3
To find the distance between the huts, we need to calculate the sum of the distances from the mast to each hut.
Distance between the huts = HM + MG
Distance between the huts = 150m / √3 + 150m
Simplifying this expression, we need to rationalize the denominator (√3) by multiplying the numerator and denominator by √3:
Distance between the huts = (150m * √3) / 3 + 150m
Distance between the huts = 50√3m + 150m
Distance between the huts = 50√3m + 150m ≈ 204.1 meters (rounded to one decimal place)
Therefore, the distance between the huts is approximately 204.1 meters.