Answer:
20.5 m North East.
Explanation:
The attached photo gives the illustration of Alan's walk.
In the attached photo, d is the total displacement of Alan's walk.
Thus, we can obtain the value of by using the cosine rule as shown:
Angle D = 138°
Side opposite D = d
Side opposite C = 12 m
Side opposite E = 10 m
d² = c² + e² – 2ce Cos D
d² = 12² + 10² – 2 × 12 × 10 × Cos 138°
d² = 144 + 100 – 240 × Cos 138°
d² = 244 – – 178.355
d² = 244 + 178.355
d² = 422.355
Take the square root of both side
d = √422.355
d = 20.5 m.
Since his new position is on a bearing of 042°, Alan' total displacement is 20.5 m North East.
