Final answer:
To find the angle between the line joining (0, -5) and (-5, 0) and the positive x-axis, we calculate the slope and use the inverse tangent function, taking into account the line lies in the fourth quadrant, giving us an angle of approximately 315 degrees.
Step-by-step explanation:
To find the angle that the lines joining the points (0, -5) and (-5, 0) make with the positive direction of the x-axis, we can use the concept of inverse tangent (arctan or tan-1). First, we identify the slope of the line connecting the two points. The slope is calculated as the change in y-coordinates divided by the change in x-coordinates, giving us m = (0 - (-5))/(-5 - 0) = 1.
Since tan(θ) = m, we have θ = tan-1(1). However, considering the points lie in the second and fourth quadrants, the reference angle made with the x-axis lies in the fourth quadrant. So, θ = 360° - tan-1(1), which is approximately 360° - 45° = 315°.
To express this in decimal form, we use a calculator to find θ = tan-1(1) to obtain an angle of 315°, which can be rounded to two decimal places if needed. Since the angle provided in the question is in degrees, if our calculator gives the result in radians, we must convert it to degrees by multiplying by 180/π.
Note: If the calculator gives a negative result, it signifies the angle is measured clockwise from the positive x-axis. However, the positive counter-clockwise angle is 360° plus the negative angle.