Question

If line segment AC = 12 and line segment BC = 10, find the measure of angle A.

Answer 1

To find the measure of angle A, we can use the Law of Cosines.

Step-by-step explanation:

To find the measure of angle A, we can use the Law of Cosines. The Law of Cosines states that for any triangle ABC, the square of the length of side AC is equal to the sum of the squares of the lengths of sides AB and BC, minus twice the product of the lengths of sides AB and BC, multiplied by the cosine of angle A.

Using the given information, we have:

AC^2 = AB^2 + BC^2 - 2(AB)(BC)cos(A)

Substituting the known values, we get:

144 = AB^2 + 100 - 2(AB)(10)cos(A)

Expanding and simplifying the equation gives us:

AB^2 - 20ABcos(A) + 44 = 0

From here, we can use the quadratic formula to solve for AB. Once we have AB, we can use the Law of Cosines again to find angle A.