Question

A car drives 12 miles north, turns, and then drives 8 miles east. How far is the car from its starting point?

a. Use the Pythagorean theorem to find the length of the missing side. Be sure to indicate which root represents the answer and write the answer in simplest radical form.
b. Use a calculator to change the answer to decimal form. Round the answer to the nearest tenth. Using this decimal number, write a sentence to explain the meaning of the answer in this situation.

Answer 1

a. Using the pythagorean theorem : c = √(a² + b²)
Let: a = 12; b = 8

Substituting the values:
c = √(12² + 8²)
c = √(144 + 64)
c = √(208)
c = √(16)(13)
c = +-4√13

The positive root indicates the answer. The car is 4√13 miles from the starting point.

b. Using a calculator to simplify c = +-4√13 in decimal form would yield:
c = 14.42 miles.

The car is now 14.42 miles away from the starting point.