a boat sails north for 3km, then sails 1,5km west. how far is the boat from its starting position? correct to two decimal

Pythagorean Theorem

3^2 + 1.5^2 = x^2

To find the distance of the boat from its starting position, we can use the Pythagorean theorem. The Pythagorean theorem states that for 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 boat has sailed north for 3 km (which is the vertical side of the triangle) and sailed 1.5 km west (which is the horizontal side of the triangle). The distance we're looking for is the length of the hypotenuse, which we can find using the following formula:

Hypotenuse = sqrt(horizontal side^2 + vertical side^2)

Plugging in the values:
Hypotenuse = sqrt(1.5^2 + 3^2)
Hypotenuse = sqrt(2.25 + 9)
Hypotenuse = sqrt(11.25)
Hypotenuse ≈ 3.35

Therefore, the boat is approximately 3.35 km from its starting position.