the diagonal of a rectangular plot is 250m long. If the length of a side is 125m, find the angle of the diagonal makes with this side
well, sin(x) = 125/250 = 1/2
look familiar?
To find the angle that the diagonal of a rectangular plot makes with one of its sides, we can use trigonometry.
Let's call the angle we want to find θ. We know that the length of the side of the rectangle is 125m, and the length of the diagonal is 250m.
First, let's draw a diagram to visualize the problem. The rectangle will have sides A, B, and the diagonal D. We want to find the angle θ between side A and the diagonal D.
We can use the Pythagorean theorem to relate the lengths of the sides of the rectangle and the diagonal:
D^2 = A^2 + B^2
Since we know the lengths of side A and the diagonal D, we can use this equation to solve for side B:
B^2 = D^2 - A^2
B^2 = 250^2 - 125^2
B^2 = 62500 - 15625
B^2 = 46875
B ≈ 216.51
Now that we know the length of side B, we can use trigonometry to find the angle θ:
θ = arctan(B/A)
θ = arctan(216.51/125)
θ ≈ 60.4 degrees
Therefore, the angle that the diagonal makes with the side of length 125m is approximately 60.4 degrees.