Find the length of side a in the right triangle if b=12 and c=15
I have the length as 6 but I don't think this is correct
Please help
a^2 + b^2 = c^2
a^2 + 144 = 225
a^2 = 81
a = √81 = 9
thank you
To find the length of side a in a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we are given the lengths of sides b and c. Let's label side a as the unknown. The Pythagorean theorem can be written as:
a^2 + b^2 = c^2
Substituting the given values, we have:
a^2 + 12^2 = 15^2
Simplifying this equation:
a^2 + 144 = 225
Next, let's isolate the variable a. Subtract 144 from both sides of the equation:
a^2 = 225 - 144
a^2 = 81
To find the value of a, we need to take the square root of both sides:
√(a^2) = √81
a = ± 9
Since side lengths cannot be negative in this context, we discard the negative value. Therefore, the length of side a is 9, not 6.
So, the correct answer is a = 9.