Final answer:
To find the value of angle x in the given triangle, we can use the Law of Sines with the known side lengths and angles. By setting up an equation and solving for sin(x), we can then find the value of angle x by taking the inverse sine.
Step-by-step explanation:
To find the value of angle x, we can use the Law of Sines. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. In this case, we have a triangle with side lengths 7.2, 4, and 7.2. Let's call the angle opposite the side length of 7.2 as angle A, and the angle opposite the side length of 4 as angle B. The angle x is opposite the side length of 7.2. Using the Law of Sines, we can set up the following equation: sin(A) / 7.2 = sin(x) / 4. Given that angle A is 32 degrees, we can rearrange the equation to solve for sin(x): sin(x) = (4 / 7.2) * sin(32). Using a calculator, we can find sin(x) to be approximately 0.6931. To find the value of angle x, we can take the inverse sine of sin(x): x = sin^(-1)(0.6931). Evaluating this expression using a calculator, we find that angle x is approximately 44.20 degrees.