Final answer:
Without additional context or information, it is not possible to accurately determine the measure of angle R. The general approach would involve using trigonometric identities and inverse trigonometric functions, typically utilizing given side lengths or vector components in calculations.
Step-by-step explanation:
To find the measure of angle R, usually given information and context are required such as a diagram or specific relationships between angles. However, going through the information provided, it seems that we are dealing with trigonometric identities and the use of a protractor to measure angles.
For example, the calculation OR = sin¹ 0.760 = 49.46º involves finding the angle whose sine value is 0.760. This is an inverse trigonometric function calculation. Similarly, we can find other angles by using inverse trigonometric functions such as tan¹ (inverse tangent) if the appropriate opposite and adjacent sides lengths are known or can be calculated.
Trigonometric identities also play a crucial role in determining angles. If one is given an expression for the resultant vector R, such as R = √ R² + R²², they might need to find the direction θ, which could be achieved with θ = tan¹ (Ry/Rx).
Given no other information or context, it is not possible to definitively choose the correct angle measure for R. More information would be necessary to solve for the angle R precisely.