Find the length of x in the 45°-45°-90° triangle. Leave your answer in simplest radical form,
side a: 9
angle b: 45°
hypotenuse: x
show work.
please answer
In a 45°-45°-90° triangle, the two legs are congruent, so if one leg is 9, the other leg is also 9.
To find the length of the hypotenuse (x), we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Substituting in the values we know:
9^2 + 9^2 = x^2
Simplifying:
81 + 81 = x^2
162 = x^2
Taking the square root of both sides:
x = √162
Simplifying:
x = 9√2
So the length of x in the 45°-45°-90° triangle is 9√2.