Right traingle ABC is graphed pm the coordinate plane and has vertices at A(-1,3), B(0,5), and C(4,3). What is the measure of angle C to the nearest degree?

F:27
G:29
H:32
J:43

To find the measure of angle C, we can use the properties of right triangles. A right triangle has one angle that measures 90 degrees. In this case, angle C is the right angle.

To find the measure of the remaining angle (angle C), we can use the tangent function. The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In this case, we have the coordinates of points A(-1,3), B(0,5), and C(4,3). To find the length of the opposite and adjacent sides, we need to calculate the differences in the y-coordinates and x-coordinates respectively.

The length of the opposite side is the difference in the y-coordinates of points B and C, which is 5 - 3 = 2.
Similarly, the length of the adjacent side is the difference in the x-coordinates of points C and A, which is 4 - (-1) = 5.

Now, we can calculate the tangent of angle C using the formula tangent(angle) = opposite/adjacent:
tangent(C) = 2/5

To find the measure of angle C, we can take the inverse tangent (or arctangent) of this value using a calculator:

angle C = arctan(2/5)

Using a calculator, we find that arctan(2/5) is approximately 22.62 degrees.

To determine the measure of angle C to the nearest degree, we round 22.62 to the nearest whole number, which is 23 degrees.

Therefore, the correct answer is not provided in the options given.