How is pythagorean theorem used

Though similar concepts had been discovered by the Babylonians, Greek Mathematician Pythagoras was the first person to come up with a geometric proof about how the sum of the squares of the lengths can determine the side lengths of a right triangle. Pythagoras determined that when three squares are arranged so that they form a right angle triangle, the largest of the three squares must have the same area as the other two squares combined. In the picture below, you can see how the sum of the squares creates the right triangle ABC.

Squares are different from other parallelograms and trapezoids because all their sides are equal lengths. So since squares are made up of four equal sides, you can see that each individual square makes up a side of the right triangle. The length of the largest square, which we'll call length c , is the length of the hypotenuse. The hypotenuse is the longest side of a right triangle. Another important application of the Pythagorean Theorem involves determining the perimeter of polygons.

Rosemary wants to plant a tulip garden in her backyard. She needs to build a triangular flowerbed using landscaping timbers. How many feet of landscaping timbers does Rosemary need to purchase?

You may have solved for x , but that does not mean we have answered the question yet. Remember that the problem asked us to determine the total length of landscaping timbers that Rosemary must purchase for her flowerbed. Use the information you know to determine the total length of landscaping timbers that Rosemary must purchase in order to completely surround her flowerbed. The Pythagorean Theorem can also be used to determine lengths of segments that may be formed by multiple right triangles or other polygons.

The Pythagorean Theorem will only work to show you the relationship between the side lengths of a right triangle. But once you know that information, you can use it to solve larger problems. A boat is sailing parallel to the shore and passes a lighthouse.

The beam from the lighthouse is visible for 14 miles. The boat passes the lighthouse along the path shown in the diagram and at its closest point is 11 miles from the lighthouse.

For how many miles will the captain of the boat be able to see the lighthouse? Use the Pythagorean Theorem to set up an equation for k. Now that you have correctly set up your equation, solve for k. Express your answer both as an irrational number and approximated to the nearest tenth of a mile. Now that we know the value of k , we can use that to answer the original question. This application is frequently used in architecture, woodworking, or other physical construction projects.

For instance, say you are building a sloped roof. If you know the height of the roof and the length for it to cover, you can use the Pythagorean Theorem to find the diagonal length of the roof's slope.

You can use this information to cut properly sized beams to support the roof, or calculate the area of the roof that you would need to shingle. The Pythagorean Theorem is also used in construction to make sure buildings are square.

A triangle whose side lengths correspond with the Pythagorean Theorem — such as a 3 foot by 4 foot by 5 foot triangle — will always be a right triangle. When laying out a foundation, or constructing a square corner between two walls, construction workers will set out a triangle from three strings that correspond with these lengths.

If the string lengths were measured correctly, the corner opposite the triangle's hypotenuse will be a right angle, so the builders will know they are constructing their walls or foundations on the right lines. The Pythagorean Theorem is useful for two-dimensional navigation. You can use it and two lengths to find the shortest distance. For instance, if you are at sea and navigating to a point that is miles north and miles west, you can use the theorem to find the distance from your ship to that point and calculate how many degrees to the west of north you would need to follow to reach that point.

The distances north and west will be the two legs of the triangle, and the shortest line connecting them will be the diagonal.