Answer:
a = 4
b = 4
Explanation:
NOTE: THIS EXPLANATION ASSUMES YOU HAVE A BASIC UNDERSTANDING OF COMMON TRIANGLES, PYTHAGOREAN THEOREM, ISOCELES TRIANGLE THEOREM, AND BASIC ALGEBRA
Since the triangle is a right triangle, and you know one of the angles is a 45 degree angle, you know the other angle is a 45 degree angle. This is a classic 45-45-90 right triangle.
If two angles are equal two each other the opposite sides of the corresponding angles are also equal each other, courtesy of the isosceles triangle theorem.
So if a = b, we can just substitute one for the other. For this explanation, I'll be using 'a' for both 'a' and 'b'.
The Pythagorean Theorem is
a^2 + b^2 = c^2
Since a = b we can say
a^2 + a^2 = c^2
Then simplify
2a^2 = c^2
Now let's just substitute the numbers
2a^2 = (4
)^2
2a^2 = 32
a^2 = 16
a = 4
Since 'a' and 'b' are equal, 'b' also equals 4.
Hope this helped! :)