Final answer:
To find the resultant for 15km east plus 20km south, use vector addition. The magnitude of the resultant can be found using the Pythagorean theorem, and the direction can be found using trigonometry. After calculating, the resultant is 'sqrt((15)^2 + (20)^2) km' at 'tan^(-1)(20/15)° south of east'.
Step-by-step explanation:
To find the resultant for 15km east plus 20km south, we need to use vector addition.
We can represent the eastward distance as a vector with a magnitude of 15km and a direction of 0° (or east). We can represent the southward distance as a vector with a magnitude of 20km and a direction of 270° (or south).
Using the Pythagorean theorem, we can find the magnitude of the resultant vector, which is the hypotenuse of a right triangle formed by the eastward and southward vectors.
We can use trigonometry to find the direction of the resultant vector. The angle can be found using the inverse tangent function: tan^(-1)(opposite/adjacent).
After calculating the magnitude and direction, we can express the resultant as 'sqrt((15)^2 + (20)^2) km' at 'tan^(-1)(20/15)° south of east'.