City a is 300km due east of cgity C 200km on a bearing of 123 form city B.how far it from C to A.
To find the distance from city C to city A, we can use the concept of vectors and trigonometry. Here's how you can calculate it:
1. Draw a diagram: Visualize the positions of the cities on a coordinate plane. Let's assume city B is the origin (0,0). City A is located 300km east of city B, so its coordinates would be (300,0). City C is located 200km from city B on a bearing of 123°, which means it forms an angle of 123° with the positive x-axis. You can draw this angle using a protractor or estimate it.
2. Find the x and y components: Calculate the x and y components of the displacement vector from city B to city C. The x component can be found by multiplying the distance (200km) by the cosine of the angle (123°). The y component can be found by multiplying the distance (200km) by the sine of the angle (123°).
x-component = 200 km * cos(123°)
y-component = 200 km * sin(123°)
3. Calculate the distance from city C to city A: To find the distance from city C to city A, we need to find the distance between their coordinates. The distance formula is the square root of the sum of the squares of the differences in the x and y coordinates.
distance CA = √[(x_A - x_C)^2 + (y_A - y_C)^2]
x_A = 300 km (x-coordinate of city A)
y_A = 0 km (y-coordinate of city A)
x_C = -x-component (x-coordinate of city C)
y_C = y-component (y-coordinate of city C)
distance CA = √[(300 km - (-x-component))^2 + (0 km - y-component)^2]
4. Substitute the values: Plug in the calculated values into the distance formula and calculate the final result.
distance CA = √[(300 - (-x-component))^2 + (0 - y-component)^2]
Simplify the expression further and calculate the result.