Marcus sails due north and Sandra sails due east from the
same starting point. In two hours, Marcus's boat is 35 miles
from the starting point and Sandra's boat is 28 miles from the
starting point. How far are the boats from each other? Round to
the nearest hundredth of a mile.

The boats are 44.82 miles from each other.

Step-by-step explanation:

The direction of movement of Marcus and Sandra forms a right angle triangle.

The distance sailed by Marcus due North would represent the opposite side of the right angle triangle.

The distance sailed by Sandra due east would represent the adjacent side of the right angle triangle.

The distance, h between the both of them after 2 hours represents the hypotenuse of the right angle triangle.

To determine h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

h² = 35² + 28² = 1225 + 784

h² = 2009

h = √2009

h = 44.82 miles

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