Question

Find the length of the unknown side round your answer to the nearest 10th

Answer 1

4.4 ft

Explanation:

The sides of a right triangle are "tied together" mathematically by an equation called the Pythagorean theorem, which says: in any right triangle, the relationship between the two sides that make the right angle (we'll call them a and b) and the side across from it (c) is

`a^2+b^2=c^2`

Let's sustitute these for the values we have in our problem (measured in feet)

`9^2+a^2=10^2\\81+a^2=100\\a^2=19\\a=√(19)`

19 is between the perfect squares
`4^2=16` and
`5^2=25`, so
`√(19)` must be between 4 and 5, a little bit closer to 4. Punching the expression into the calculator confirms this with a value of
`√(19)\approx4.3588` which we can round to 4.4 ft.