Question

A boat travels 21 miles due north and then 28 miles due east. Then the boat travels in a straight line back to its starting point. What was the straight line distance of the boat to its starting point?

Answer 1

When the boat headed 21 miles north then 28 miles to the east then back to its starting point, it formed a right angle triangle. And that straight line the question is talking about is the hypotenuse.

Use the Pythagorean Theorem to solve for hypotenuse.

The Pythagorean Theorem states that for any right triangle the following is true: when you take the sum of both of the legs squared it will equal to the hypotenuse squared.

In equation form: $a^2 + b^2 = c^2$

Where the variables a and b are the legs. And the variable c is the hypotenuse.

Plug in the values.

$21^2 + 28^2 = c^2$
$441 + 784 = c^2$
$1225 = c^2$
35 = c

So, the straight line is 35 miles long.