# What are some real life examples of the pythagorean theorem?

Jun 13, 2018
• When carpenters want to construct a guaranteed right angle, they can make a triangle with sides 3, 4, and 5 (units). By the Pythagorean Theorem, a triangle made with these side lengths is always a right triangle, because ${3}^{2} + {4}^{2} = {5}^{2.}$

• If you want to find out the distance between two places, but you only have their coordinates (or how many blocks apart they are), the Pythagorean Theorem says the square of this distance is equal to the sum of the squared horizontal and vertical distances. ${d}^{2} = {\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}$

Say one place is at $\left(2 , 4\right)$ and the other is at $\left(3 , 1\right)$. (These could also be latitude and longitudes, but you get the idea.) Then we square the horizontal distance:

${\left(2 - 3\right)}^{2} = 1$

and the vertical distance:

${\left(4 - 1\right)}^{2} = 9$

$1 + 9 = 10$

and then take the square root.

$d = \sqrt{10}$

• TV sizes are measured on the diagonal; it gives the longest screen measurement. You can figure out what size TV can fit in a space by using the Pythagorean Theorem:

${\left(\text{TV size")^2 = ("space width")^2 + ("space height}\right)}^{2}$

Note: you should also remember that TVs are usually $16 \times 9 ,$ so you'd likely want to measure just the width of the space, then use $\text{width } \times \frac{9}{16}$ as the height of the space.