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.
We can use the Law of Cosines to find the measure of angle ∠A in the oblique triangle ABC.
The Law of Cosines states that for any triangle with sides of lengths a, b, and c and angles A, B, and C opposite those sides:
c^2 = a^2 + b^2 - 2abcosC
In this case, the sides are given as follows:
a = 13 m
b = 6 m
c = 9 m
We are trying to find angle A, so we will use side c as angle A's opposite side.
Plugging the given values into the Law of Cosines equation, we have:
9^2 = 13^2 + 6^2 - 2(13)(6)cosA
81 = 169 + 36 - 156cosA
81 = 205 - 156cosA
-124 = -156cosA
cosA = (-124)/(-156)
cosA = 0.7949
Now, to find the measure of angle A, we need to take the inverse cosine of 0.7949:
A = cos^-1(0.7949) ≈ 37.3 degrees
Therefore, the measure of angle ∠A is approximately 37.3 degrees.