an airplane flew from a city x on a bearing 225 to another city y a distance 200 km away.It then flew from city y on a bearing of N30 W to city Z a distance of 250 km. calculate
1.the distance from city x to city z correct to the nearest whole number.
2. the bearing of a city x from city z.
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Well, let's clown our way through these calculations!
1. To find the distance from city X to city Z, we'll create a triangle using the given information. We know that the distance from X to Y is 200 km, and the distance from Y to Z is 250 km.
Now, we can use the good old Pythagorean theorem (a^2 + b^2 = c^2) to find the distance from X to Z. Here we go:
XZ^2 = XY^2 + YZ^2
XZ^2 = 200^2 + 250^2
XZ^2 = 40000 + 62500
XZ^2 = 102500
XZ ≈ √102500
XZ ≈ 320.5 km
The distance from city X to city Z, rounded to the nearest whole number, is approximately 321 km.
2. To find the bearing of city X from city Z, we need to use some clown geometry!
First, let's establish a reference direction. Since X is 225 degrees away from Y, we'll consider East as our reference direction, which is 0 degrees.
Next, we'll determine the angle made by the line connecting X and Z with respect to this reference direction. City Y is at a bearing of N30 W, which is equivalent to 330°.
So, let's calculate the bearing:
Bearing of X from Z = 225° + 180° - 330°
Bearing of X from Z ≈ 75°
The bearing of city X from city Z is approximately 75 degrees (and a splash of clown logic).
Hope that brings a smile to your face!
To solve this problem, we can use the concept of vector addition and trigonometry.
1. Distance from city x to city z:
To find the distance from city x to city z, we need to find the components of the distances traveled in the north-south and east-west directions.
First, let's break down the distance traveled from city x to city y:
Given:
Bearing of 225 degrees
Distance of 200 km
To find the east-west component (Ex1) and north-south component (Ey1), we can use trigonometry:
Ex1 = cos(225) * 200 km
Ey1 = sin(225) * 200 km
Next, let's break down the distance traveled from city y to city z:
Given:
Bearing of N30 W (330 degrees)
Distance of 250 km
To find the east-west component (Ex2) and north-south component (Ey2), we can use trigonometry:
Ex2 = cos(330) * 250 km
Ey2 = sin(330) * 250 km
Now, let's add the east-west and north-south components together to find the total displacement:
Total Ex = Ex1 + Ex2
Total Ey = Ey1 + Ey2
Finally, we can use the Pythagorean theorem to find the total distance from city x to city z:
Distance = √(Total Ex^2 + Total Ey^2)
Plugging in the values and calculating, you can find the distance from city x to city z correct to the nearest whole number.
2. Bearing of city x from city z:
To find the bearing of city x from city z, we need to calculate the angle between the line connecting the two cities and the north direction.
First, let's find the total displacement angle:
Displacement angle = atan(Total Ey / Total Ex)
Next, we need to adjust the angle based on the quadrant in which city x lies:
If Total Ex > 0 (city x is to the east of city z):
Bearing = 90 degrees - Displacement angle
If Total Ex < 0 (city x is to the west of city z):
Bearing = 270 degrees - Displacement angle
Now, you can calculate the bearing of city x from city z.
I don't know it
All angles are measured CW from +y-axis.
1. D = 200km[225o] + 250km[330o].
X = 200*sin225 + 250*sin330 = -266.4 km.
Y = 200*Cos225 + 250*Cos330 = 75.1 km.
D = -266.4 + 75.1i = 277km[-74.3] = 277km[285.6o] CW.
2. Tan A = X/Y.
A = ?