Find the gradient of the line joining (3,7) and (6,9).Hence, find the acute angle it makes with the positive x- axis.
Sure I know how to find the gradient but I don't know how to find the acute angle in a case like this
Ok, ok, you have now asked 4 questions without giving me any idea where your difficulties lie, or what effort you have made to solve these problems.
We do not do a student's homework here.
e.g. Surely you know how to find the slope or "gradient" between two given points.
You should also know that tanθ = slope, where θ is the angle that the line makes with the x-axis
M=change in y ÷change in x
To find the gradient of a line, we need to use the formula:
Gradient (m) = (y2 - y1) / (x2 - x1)
In this case, the points are (3, 7) and (6, 9). Let's assign the coordinates as follows:
(x1, y1) = (3, 7) and (x2, y2) = (6, 9)
Now we can substitute these values into the formula:
m = (9 - 7) / (6 - 3)
m = 2 / 3
So, the gradient of the line is 2/3.
To find the acute angle the line makes with the positive x-axis, we can use the inverse tangent function (arctan) since the gradient (m) is equal to the tangent of the angle. The formula is:
Angle (θ) = arctan(m)
Substituting the value of m into the formula:
θ = arctan(2/3)
Now you can use a scientific calculator or online tool to find the arctan(2/3) value.
After calculating, you will get the acute angle that the line makes with the positive x-axis.