Find the missing leg sides already given 15 and 9 find missing bottom a

Answer 1

To find the length of the missing side (let's call it $a$) of a right triangle given the lengths of the other two sides (15 and 9), you can use the Pythagorean theorem. The theorem states that in a right triangle:

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

where $c$ is the length of the hypotenuse (the longest side), and $a$ and $b$ are the lengths of the other two sides.

1. If 15 is the hypotenuse and 9 is one leg, you can set it up as follows:

$$9^2+a^2={15}^2$$

Calculating the squares:

$$81+a^2=225$$

Now, solve for $a^2$:

$$a^2=225-81$$ $$a^2=144$$

Now, take the square root of both sides:

$$a=\sqrt{144}$$ $$a=12$$

So in this case, the missing leg ($a$) is 12.

2. If instead, 15 is one leg and 9 is the other leg, we would set it up as:

$${15}^2+9^2=a^2$$

Calculating the squares:

$$225+81=a^2$$

Now, solve for $a^2$:

$$a^2=306$$

Now, take the square root of both sides:

$$a=\sqrt{306}$$ $$a\approx 17.44$$

In conclusion:

• If 15 is the hypotenuse, the missing leg $a$ is 12.
• If 15 is one leg, the missing side $a$ is approximately 17.44.

You would need to clarify which side is the hypotenuse for a definitive answer.