Question

After walking due west turning and walking due south a man is 900m from his starting point and bearing 205 degrees from it. How far did he walk westward and southward?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let the distance the man walked due west be x meters and the distance he walked due south be y meters.

From the information given, we can set up the following equations:

x^2 + y^2 = 900^2 (Pythagorean theorem)
tan(205°) = y/x

First, let's find x and y using the second equation.

tan(205°) = y/x
-3.7321 = y/x
y = -3.7321x

Now substitute y = -3.7321x into the first equation.

x^2 + (-3.7321x)^2 = 900^2
x^2 + 13.946x^2 = 810000
14.9461x^2 = 810000
x^2 = 810000 / 14.9461
x^2 ≈ 54250.14
x ≈ 232.97 m

Now, we can find y.

y = -3.7321(232.97)
y ≈ -868.23 m

Therefore, the man walked approximately 232.97 meters due west and approximately 868.23 meters due south.