Find total displacement. 10 points. Will give brainliest!

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.

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