To find the length of AB, we can use the Pythagorean theorem.
Given that AB = 8 and tan^2(BAC) = √5 / 2, we can calculate the length of AC by taking the square root of (√5 / 2)^2.
Since tan(BAC) = AC/AB, we have tan(BAC) = AC / 8.
Solving for AC, we get AC = 8 tan(BAC) = 8 √5 / 2 = 4√5.
Now, we can use the Pythagorean theorem to find the length of AB:
AB^2 = AC^2 + BC^8^2 = (4√5)^2 + BC^64 = 80 + BC^BC^2 = 64 - 8BC^2 = -16
Since BC is a length, it cannot be negative, so there seems to be an error in the given information. It is not possible to determine the exact length of AB under these conditions.
To find the length of AB, we can use the Pythagorean theorem.
Given that AB = 8 and tan^2(BAC) = √5 / 2, we can calculate the length of AC by taking the square root of (√5 / 2)^2.
Since tan(BAC) = AC/AB, we have tan(BAC) = AC / 8.
Solving for AC, we get AC = 8 tan(BAC) = 8 √5 / 2 = 4√5.
Now, we can use the Pythagorean theorem to find the length of AB:
AB^2 = AC^2 + BC^
8^2 = (4√5)^2 + BC^
64 = 80 + BC^
BC^2 = 64 - 8
BC^2 = -16
Since BC is a length, it cannot be negative, so there seems to be an error in the given information. It is not possible to determine the exact length of AB under these conditions.