Final answer:
To find the angle between the longer side and the diagonal of a rectangle, we can use the properties of a rectangle and the Pythagorean theorem. The angle is approximately 23.6 degrees.
Step-by-step explanation:
To find the angle between the longer side and the diagonal of a rectangle, we can use the properties of a rectangle and the Pythagorean theorem. In a rectangle, the diagonals are equal in length and bisect each other. Therefore, we can split the rectangle into two right triangles. Let's label the longer side of the rectangle as 'a', the shorter side as 'b', and the diagonal as 'd'.
Using the Pythagorean theorem, we have:
d^2 = a^2 + b^2
Substituting the given values, we have:
(25)^2 = (10)^2 + b^2
Solving for b, we get:
b^2 = (25)^2 - (10)^2
b^2 = 625 - 100
b^2 = 525
b = sqrt(525)
b ≈ 22.91
Now we can use trigonometry to find the angle between the longer side and the diagonal. Let's label this angle as 'θ'. We have:
sin(θ) = a/d
sin(θ) = 10/25
sin(θ) = 0.4
θ = arcsin(0.4)
θ ≈ 23.6 degrees