A city B is 205km from a
village C on a bearing 035˚, how
far is B cast of C?
A. 205km
B. 146km
C. 117.6km
D. 91.7km
To find the distance between B and C, we need to use trigonometry.
First, we can split the 035˚ bearing into its component angles.
The angle in the x-direction (east) is 90˚ - 35˚ = 55˚.
The angle in the y-direction (north) is 35˚.
Using the sine and cosine functions, we can calculate the distances in each direction.
distance in the x-direction = 205km * cos(55˚) ≈ 205km * 0.5736 ≈ 117.6km
Therefore, B is approximately 117.6 km east of C.
The answer is C. 117.6km.
To find the distance from city B to village C, we can use trigonometry.
Since the bearing is given as 035˚, we can consider it as an angle of a right triangle. The distance from B to C is the adjacent side, and the distance we need to find is the hypotenuse.
Using the trigonometric ratio cosine (cos), we can find the adjacent side (AC):
cos(angle) = adjacent/hypotenuse
cos(35˚) = AC/205km
Solving for AC:
AC = 205km * cos(35˚)
AC ≈ 168.66km
Therefore, city B is approximately 168.66km east of village C.
The closest answer choice is:
C. 117.6km