This can be solved with the Pythagorean Theorem.  

6² + 4² = c²

52 = c²

c = √52 = 2√13

By drawing Angela’s route, we can connect her end point and her start point with a straight line and will then have a right triangle. The Pythagorean theorem can be used to solve for how far she is from the starting point: a²+b²=c², 30²+40²=c², c=50. It can also be noted that Angela’s route represents a multiple of the 3-4-5 Pythagorean triple.

Since east and north directions are perpendicular, the possible routes Bob can take can be represented by a right triangle with sides a and b of length 3 miles and 5 miles, respectively. The hypotenuse c represents the straight line connecting his house to the store, and its length can be found using the Pythagorean theorem: c² = 3²+ 4² = 25. Since the square root of 25 is 5, the length of the hypotenuse is 5 miles.

This question requires the use of Pythagorean Theorem. We are given the length of two sides of a triangle and asked to find the third. We are told that the two sides we are given meet at a right angle, this means that the missing side is the hypotenuse. So we use a² + b² = c², plugging in the two known lengths for a and b. This yields an answer of 27.46 feet.

Kathy's path traces the outline of a right triangle with legs of 6 and 8. By using the Pythagorean Theorem

miles

Jeff drives a total of 10 miles north and 10 miles east.  Using the Pythagorean theorem (a²+b²=c²), the direct route from Jeff’s home to his work can be calculated.  10²+10²=c².  200=c². √200=c. √100Ÿ√2=c. 10√2=c

By using Pythagorean Theorem, we can solve for the distance “as the crow flies” from Jim to his home:

10² + 5² = x²

100 + 25 = x²

√125 = x, but we still need to factor the square root

√125 = √25*5, and since the √25 = 5, we can move that outside of the radical, so

5√5= x

Distance = hours * mph

North Distance = 5 hours * 60 mph = 300 miles

East Distance = 2 hours * 50 mph = 100 miles

Use Pythagorean Theorem to determine Northeast Distance

300^{2 +} 100² =NE²

90000  + 10000 = 100000 = NE²

NE = √100000

A right triangle can be drawn between the airplane and its destination.

                           Destination

                      15 miles    Airplane

                                     8 miles

We can solve for the hypotenuse, x, of the triangle:

8² + 15² = x²

64 + 225 = x²

289 = x²

x = 17 miles

The distances when put together create a right triangle.  

The distance between them will be the hypotenuse or the diagonal side.  

You use Pythagorean Theorem or  to find the length.  

So you plug  and  for  and  which gives you,

  or .  

Then you find the square root of each side and that gives you your answer of .