Final answer:
Given right triangle BAC, mLA = 90, mLB = 45, and AC = 8, the length of side BC is B. 8√2.
Step-by-step explanation:
In this right triangle, we know that angle LBA is 45 degrees and angle LCA is 90 degrees.
To find the length of side BC, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, side AC is the hypotenuse and sides AB and BC are the other two sides.
Let's denote the length of side BC as x. Using the Pythagorean theorem, we can set up the following equation:
(AB)² + (BC)² = (AC)²
Since AB is equal to x and AC is equal to 8, we can rewrite the equation as:
x² + (BC)² = 8²
Since we know that angle LBA is 45 degrees, ABC is an isosceles right triangle.
That means side AB and side BC have the same length. So we can rewrite the equation as:
x² + x² = 64
Combining like terms, we get:
2x² = 64
Dividing both sides by 2, we have:
x² = 32
Taking the square root of both sides, we find:
x = √32
x = 8√2
So therefore the correct answer is B. 8√2