If in oblique ΔABC side a=13 m, side b=6 m, and side c=9 m, then use the Law of Cosines to find the measure of ∠A .(1 point) Responses 50 degrees 50 degrees 63 degrees 63 degrees 15 degrees 15 degrees 119 degrees 119 degrees

Answer 1

To find the measure of angle A, we can use the Law of Cosines. The formula is as follows:

c^2 = a^2 + b^2 - 2ab*cos(A)

In this case, we know the values of sides a, b, and c. Plugging in the values into the formula, we get:

9^2 = 13^2 + 6^2 - 2(13)(6)*cos(A)

81 = 169 + 36 - 156*cos(A)

81 = 205 - 156*cos(A)

156*cos(A) = 205 - 81

156*cos(A) = 124

cos(A) = 124/156

Now, we can use inverse cosine (cos^(-1)) to find the angle A:

A = cos^(-1)(124/156)

A ≈ 50 degrees

Therefore, the measure of angle A is approximately 50 degrees.