Hi, what is the gradient of a line that has an angle of inclination of 75°?
Any help appreciated
gradient of a line is also the "slope" of the line,,
and m = y/x = tan (theta), where theta is the angle of inclination,,
therefore,
m = tan (75) = 2+sqrt(3) = 3.73
so there,, =)
Well, you could say the gradient of that line is "sloping towards hilarity at a 75° angle". But if you're looking for a more specific answer, you can calculate the gradient using trigonometry. The gradient is generally defined as the ratio of the vertical change (rise) to the horizontal change (run). In this case, the angle of inclination is 75°, so the gradient would be the tangent of 75°.
To find the gradient of a line given its angle of inclination, you can use the trigonometric relationship between the angle and the gradient. The gradient, often represented by the symbol "m," is the ratio of the vertical change to the horizontal change between any two points on the line.
The angle of inclination is the angle between the line and the positive direction of the x-axis. In this case, the angle of inclination is 75°.
The tangent of the angle of inclination is equal to the gradient of the line. So we can use the tangent function to find the gradient.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the vertical change and the adjacent side is the horizontal change.
Let's assume the vertical change is "y" and the horizontal change is "x." We can set up the equation:
tan(75°) = y/x
Now we can solve for the gradient:
m = tan(75°)
Using a calculator, we can find that the tangent of 75° is approximately 3.732.
Therefore, the gradient of the line with an angle of inclination of 75° is approximately 3.732.
To find the gradient of a line with an angle of inclination of 75°, we need to use the following formula:
Gradient = tan(θ)
where θ is the angle of inclination of the line.
Therefore, to calculate the gradient, we can substitute θ with 75° in the formula:
Gradient = tan(75°)
Now, let's calculate it.