Answer:
a = √63
Explanation:
Pre-Solving
We are given a right triangle (notice the right angle).
We know that the hypotenuse (the side opposite of the right angle) is 12.
We also know that one leg (a side that makes up the right angle) is 9, and that the other one is a.
We want to find what a is.
Solving
We can use the Pythagorean Theorem to help us find a.
The Pythagorean Theorem says a² + b² = c², where a and b are the legs and c is the hypotenuse.
Since we already know the values of the legs and hypotenuse, we can substitute these values in the theorem, but let's first label the values of everything to avoid confusion / mistakes.
a = a
b = 9
c = 12
Now, plug into the formula.
a² + 9² = 12²
Simplify:
a² + 81 = 144
Subtract 81 from both sides
a² = 63
Square root both sides to get the value of a.
a = √63