Question

A boat leaves the dock and travels 5 miles due south, then 12 miles due west How far is the boat from the dock?

Answer 1

Answer:

13 miles

Step-by-step explanation:

This problem can be represented as a right angle triangle (shown in the diagram).

The distance of the boat from the dock is the hypotenuse of the triangle, hence, we need to find the hypotenuse of the triangle. To do this, we apply Pythagoras theorem:

$hyp^2 = opp^2 + adj^2$

where opp = side opposite angle of consideration = 12 miles

adj = side adjacent angle of consideration = 5 miles

Hence:

$hyp^2 = 12^2 + 5^2\\\\\\hyp^2 = 144 + 25 = 169\\\\\\hyp = \sqrt{169}\\ \\\\hyp = 13 miles$

The boat is therefore, 13 miles from the dock.