Final answer:
To find the measure of ∠R in △RST, we can use the Law of Cosines and the given lengths of the sides of the triangle. Substitute the values into the formula to find the cosine of ∠R. Take the inverse cosine to find the measure of ∠R.
Step-by-step explanation:
To find the measure of ∠R in triangle RST, we can use the Law of Cosines. The Law of Cosines states that a² = b² + c² - 2bc * cos(A), where a, b, and c are the lengths of the sides of the triangle, and A is the angle opposite side a. In this case, side a is RT, side b is ST, side c is RS, and angle A is ∠R.
Using the given values, we can substitute them into the formula:
R² = (6.5)² + (8.9)² - 2(6.5)(8.9) * cos(∠R)
Now, we can solve for cos(∠R):
cos(∠R) = (6.5² + 8.9² - 4.3²) / (2(6.5)(8.9))
Finally, we can find the measure of ∠R by taking the inverse cosine of cos(∠R) using a calculator.