Question

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
50 degrees
50 degrees

63 degrees
63 degrees

119 degrees
119 degrees

15 degrees

Answer 1

To use the Law of Cosines to find the measure of ∠A, we can use the following formula:

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

Given that a = 13, b = 6, and c = 9, we can substitute these values into the formula:

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

81 = 169 + 36 - 156 cos(A)

Combine the like terms:

81 = 205 - 156 cos(A)

Rearrange the equation to solve for cos(A):

156 cos(A) = 205 - 81

156 cos(A) = 124

cos(A) = 124/156

cos(A) ≈ 0.794

Now, we can find the measure of ∠A by taking the inverse cosine (cos^-1) of 0.794. This can be done using a calculator or a mathematical software:

∠A ≈ cos^-1(0.794)

∠A ≈ 38.568 degrees

Therefore, the measure of ∠A is approximately 38.568 degrees.