To find the measure of angle x, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides of length a, b, and c and angles A, B, and C (opposite those sides), the following relationship holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we have a = 12, b = 18, and C = 38°. We need to find side c first:
c^2 = 12^2 + 18^2 - 2 * 12 * 18 * cos(38°)
c^2 = 144 + 324 - 432 * cos(38°)
c ≈ 15.98 (using a calculator to compute the cosine and square root)
Now, we can use the Law of Cosines again to find the measure of angle x:
cos(x) = (12^2 + 15.98^2 - 18^2) / (2 * 12 * 15.98)
cos(x) ≈ 0.3894 (using a calculator to compute)
Now, we find the inverse cosine (arccos) to get x:
x ≈ arccos(0.3894)
x ≈ 67° (to the nearest degree)
What is the measure of x in the triangle below? Round to the nearest degree.
scalene triangle:
side 1: 12
side 2: 18
vertex: 38°
you should get 67°
please answer
1 answer
1 answer