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 .

This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that  

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

In this equation:

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

In this equation:

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

In this equation:

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

In this equation:

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs: