To find the measure of ∠BAC, we can use the law of cosines, which states that:
c^2 = a^2 + b^2 - 2ab cos(C)
Where c is the length of the side opposite angle C. In this case, we have:
c = 8
a = 7
b = 5
Substituting these values, we get:
8^2 = 7^2 + 5^2 - 2(7)(5) cos(C)
Simplifying:
64 = 49 + 25 - 70 cos(C)
70 cos(C) = 10
cos(C) = 10/70
cos(C) = 1/7
Using a calculator, we can find that the arccosine of 1/7 is approximately 82.46 degrees. Therefore, the measure of ∠BAC is approximately:
∠BAC = 180 - ∠ABC - ∠ACB
∠BAC = 180 - 90 - 82.46
∠BAC = 7.54 degrees (rounded to two decimal places)
So the measure of angle ∠BAC is approximately 7.54 degrees.