a boy travels 15 km due north,then goes 9 km due east,then 3km due south.how far is he from his starting point
15 km
15
To find the distance from the boy's starting point, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the boy's travel forms a right-angled triangle. The distance traveled north and south represents the two legs of the triangle, and the distance traveled east represents the hypotenuse.
Let's calculate the distances traveled north and south:
Distance traveled north = 15 km
Distance traveled south = 3 km
Now, we can calculate the hypotenuse (distance traveled east) using the Pythagorean theorem:
Hypotenuse^2 = (Distance traveled north)^2 + (Distance traveled south)^2
Hypotenuse^2 = 15^2 + 3^2
Hypotenuse^2 = 225 + 9
Hypotenuse^2 = 234
To find the length of the hypotenuse (distance traveled east), we take the square root of both sides:
Hypotenuse = √234
Hypotenuse ≈ 15.297 km
Therefore, the boy is approximately 15.297 km away from his starting point.