A rectangle has sides 170mm and 130mm.What is the angle between the diagonals?
tanθ = 130/170 or, for the other angle,
tanθ = 170/130
sorry; that's the angle between the diagonal and a side of the rectangle.
so, draw a diagram, and the angle you want is Ø, where
2θ+Ø = 180
To find the angle between the diagonals of a rectangle, we can use the formula:
angle = arccos(a/b)
where:
a = length of one side
b = length of the other side
In this case, the sides of the rectangle are 170mm and 130mm.
Let's calculate the angle:
angle = arccos(170/130)
Using a calculator, we can find the value of arccos(170/130) to be approximately 1.004 rad.
Therefore, the angle between the diagonals of the rectangle is approximately 1.004 radians.
To find the angle between the diagonals of a rectangle, you can use trigonometric functions.
First, let's label the sides of the rectangle and the angles between the diagonals:
- Side A = 170 mm
- Side B = 130 mm
- Diagonal 1 = D1
- Diagonal 2 = D2
- Angle between Diagonals = θ
To find the angle θ, we can use the formula:
θ = arctan(D1/D2)
Now, let's calculate the lengths of the diagonals:
- D1 can be found using the Pythagorean theorem, as it forms a right triangle with sides A and B:
D1 = √(A^2 + B^2)
D1 = √(170^2 + 130^2)
Using a calculator to do the calculation, we get:
D1 ≈ 215.396 mm (rounded to three decimal places)
- D2 is equal to the length of the other diagonal of the rectangle, so D2 = 170 mm.
Now, let's substitute the values into the formula to calculate the angle θ:
θ = arctan(D1/D2)
θ = arctan(215.396 / 170)
Using a calculator or arctan table, we find that:
θ ≈ 51.95 degrees (rounded to two decimal places)
Therefore, the angle between the diagonals of the rectangle is approximately 51.95 degrees.