Question

The Pythagorean theorem Find each missing length to the nearest length

Answer 1

To find any missing length in a right triangle, we use the Pythagorean Theorem:

$a^2=b^2+c^2$

Where a is the length of the hypotenuse, the longest side.

In the given right triangle:

• a=8.9

,

• b=4

,

• c=8

We check if this satisfies the Pythagorean Theorem:

$\begin{gathered} a^2=4^2+8^2 \\ a^2=16+64 \\ a^2=80 \\ a=\sqrt[]{80} \\ a=8.9\text{ units} \end{gathered}$

Thus, we see that the Pythagorean Theorem holds.