Question

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

Answer 1

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)