Final answer:
The approximate measure of angle C in Triangle RST is 90 degrees, as line BC is vertical and line AC has a slope of -9/5, indicating a right angle at point C.
Step-by-step explanation:
The given coordinates of the vertices of Triangle RST are A(3,3), B(8,3), and C(8,-6). To find the approximate measure of angle C, we will use the concept of the slope of a line and trigonometric functions.
Finding the Slope
The slope of line BC is determined by the change in y divided by the change in x between point B and C. As points B and C have the same x-coordinate, the slope of BC is undefined, which means BC is a vertical line. Similarly, the slope of line AC can be found by taking the difference in y-coordinates of points A and C and dividing by the difference in x-coordinates of the same points.
Slope of AC = (y2 - y1) / (x2 - x1) = (-6 - 3) / (8 - 3) = -9 / 5.
Calculating Angle C
To find angle C, we can use the arctangent function, which gives us the angle whose tangent is the slope of AC. Therefore, we calculate:
Angle C = arctan(Slope of AC) = arctan(-9 / 5).
However, since BC is a vertical line and AC has a negative slope, angle C is a right angle (90 degrees). Therefore, the measure of angle C is approximately 90 degrees.