A rectangle has sides of length 2.2m and 8m longer calculate the angle between a diagonal
We start by using the Pythagorean theorem to find the length of the diagonal of the rectangle:
d² = (2.2m)² + (8m + 2.2m)²
d² = 4.84m² + 72.36m²
d² = 77.2m²
d ≈ 8.79m
Next, we can use trigonometry to find the angle between the diagonal and the shorter side of the rectangle. Let's call this angle θ. We can use the cosine function to do this:
cos(θ) = adjacent / hypotenuse
cos(θ) = 2.2m / 8.79m
θ = cos⁻¹(0.25)
θ ≈ 75.52°
Therefore, the angle between the diagonal and the shorter side of the rectangle is approximately 75.52 degrees.
To calculate the angle between the diagonal of a rectangle, we can use the Pythagorean theorem and trigonometric functions.
Step 1: Find the length of the diagonal.
Using the Pythagorean theorem, we can calculate the diagonal using the length of the sides of the rectangle.
diagonal^2 = side1^2 + side2^2
Given:
side1 = 2.2m
side2 = 2.2m + 8m = 10.2m
Plugging in the values:
diagonal^2 = (2.2m)^2 + (10.2m)^2
Simplifying:
diagonal^2 = 4.84m^2 + 104.04m^2
diagonal^2 = 108.88m^2
Finding the square root of both sides:
diagonal ≈ √108.88m^2
diagonal ≈ 10.44m
Step 2: Calculate the angle between the diagonal.
Now that we have the length of the diagonal, we can use trigonometric functions to find the angle.
cos(angle) = adjacent/hypotenuse
Given:
adjacent = side1 = 2.2m
hypotenuse = diagonal = 10.44m
Plugging in the values:
cos(angle) = 2.2m / 10.44m
Calculating the angle using the inverse cosine function (arccos):
angle = arccos(2.2m / 10.44m)
angle ≈ 74.48°
The angle between the diagonal of the rectangle is approximately 74.48 degrees.