A rectangle has sides of length 2.2m and 8m Calculate the angle between a diagonal and a longer side
To find the angle between a diagonal and a longer side of a rectangle, we can use the trigonometric function called tangent (tan).
1. Start by finding the length of the diagonal of the rectangle using the Pythagorean theorem:
diagonal^2 = shorter side^2 + longer side^2
diagonal^2 = 2.2^2 + 8^2
diagonal^2 = 4.84 + 64
diagonal^2 = 68.84
diagonal ≈ √68.84
diagonal ≈ 8.298 m
2. Now, we can find the angle by calculating the inverse tangent (arctan) of the quotient between the longer side and the diagonal:
angle = arctan(longer side / diagonal)
angle = arctan(8 / 8.298)
Using a calculator or the trigonometric table for arctan, we find:
angle ≈ 55.6 degrees
Therefore, the angle between the diagonal and the longer side of the rectangle is approximately 55.6 degrees.