A rectangle has sides of length 2.2m and 8m Calculate the angle between a diagonal

1 answer

To find the angle between the diagonal and one of the sides, we can use the formula:

cos(theta) = adjacent/hypotenuse

where theta is the angle between the diagonal and the side, adjacent is the length of the side adjacent to the angle, and hypotenuse is the length of the diagonal.

In this case, let's consider the diagonal that connects the opposite corners of the rectangle. This diagonal forms a right triangle with the two sides of the rectangle.

Using the Pythagorean theorem, we can find the length of the diagonal:

d^2 = 2.2^2 + 8^2
d^2 = 4.84 + 64
d^2 = 68.84
d = 8.299

Now, let's find the angle between the diagonal and the 2.2m side. We'll call this angle x.

cos(x) = 2.2/8.299
x = cos^-1(2.2/8.299)
x = 72.36 degrees (rounded to 2 decimal places)

Therefore, the angle between the diagonal and the 2.2m side is approximately 72.36 degrees.