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
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.