18. A city B is 205km from a
village C on a bearing 035°, how
far is B east of C?
A. 205km
B. 146km
C. 117.6km
To find the distance east, we can use the trigonometric ratio of the angle between the bearing and the east direction.
The angle between the bearing and the east direction is 90° - 35° = 55°.
Now, we can use the cosine function to find the distance east:
Distance east = Distance x cos(angle)
Distance east = 205km x cos(55°)
Distance east ≈ 205km x 0.5736
Distance east ≈ 117.6km
Therefore, the distance B is east of C is approximately 117.6km.
Option C is correct.
To find how far city B is east of village C, we need to resolve the bearing of 035° into its north and east components.
First, we need to determine the east component. The east component is given by the formula: East = distance x sin(bearing).
Given that the distance is 205km and the bearing is 035°, the east component is:
East = 205km x sin(35°)
East ≈ 205km x 0.5736
East ≈ 117.6km
Therefore, city B is approximately 117.6km east of village C.
The correct answer is C. 117.6km.