Question

If the length of one leg of a right triangle is 3 and the hypotenuse is $\sqrt{34}$, what is the length of the other leg?

Answer 1

$\huge{\boxed{5}}$

The Pythagorean theorum states that when $a$ and $b$ are sides and $c$ is the hypotenuse, $a^2 + b^2 = c^2$

So, let's plug in the values. $3^2 + b^2 = (\sqrt{34})^2$

Simplify. The square of a square root is the number inside the square root. $9 + b^2 = 34$

Subtract 9 from both sides. $b^2 = 25$

Get the square root of both sides. $\sqrt{b^2} = \sqrt{25}$

$b=\boxed{5}$

Answer 2

Answer:

5

Step-by-step explanation:

Use the Pythagorean theorem:

$leg^2+leg^2=hypotenuse^2$

We have

$leg=3,\ hypotenuse=\sqrt{34}$

Let's mark the other leg as x.

Substitute:

$3^2+x^2=(\sqrt{34})^2$      use (√a)² = a

$9+x^2=34$            subtract 9 from both sides

$x^2=25\to x=\sqrt{25}\\\\x=5$