Question

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

Answer 1

Answer:

4.4 ft

Step-by-step 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)

$9^2+a^2=10^2\\81+a^2=100\\a^2=19\\a=\sqrt{19}$

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