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°

Answer 1

Let's use the Law of Cosines to solve for the measure of angle x.

cos(x) = (side 1^2 + side 2^2 - opposite side^2) / (2 * side 1 * side 2)

First, we need to find the length of the opposite side to angle x. Let's call it side 3. We can use the Law of Sines to solve for side 3.

(side 3) / sin(38°) = (side 1) / sin(x)

Now, we can substitute side 1 and side 2 to find the length of side 3.

side 3 = (side 1 * sin(38°)) / sin(x)

Now, we can plug in the values of side 1 and side 2 into the Law of Cosines equation:

cos(x) = (12^2 + 18^2 - ((12 * sin(38°)) / sin(x))^2) / (2 * 12 * 18)

cos(x) ≈ 0.499

x ≈ cos^(-1)(0.499) ≈ 60°

The measure of x is approximately 60°.