A rectangle has sides 170mm and 130mm.What is the angle between the diagonals?
look at triangle of altitude (13/2) = 6.5 and base (17/2) = 8.5
x = half of angle between diagonals.
tan x = 8.5/6.5
x = 52.6
2x = big angle between diagonals = 105.3 degrees
small angle between diagonals = 180 - 105.3 = 74.8 degrees
Well, it seems like the rectangle is feeling a little "acute" today! To find the angle between the diagonals, let's first think about the properties of a rectangle. In a rectangle, the diagonals are congruent, meaning they have the same length.
Using Pythagoras, we can find the length of the diagonal. Given the sides of the rectangle are 170mm and 130mm, we can calculate it as follows:
diagonal length = √(170^2 + 130^2)
diagonal length = √(28900 + 16900)
diagonal length = √45800
diagonal length ≈ 214.04mm
Now, since the diagonals of a rectangle bisect each other and are congruent, we can think of the rectangle being divided into four right triangles. Therefore, the angle between the diagonals would be the same as the angle in one of these right triangles.
By employing a bit of trigonometry, we can find the angle:
tan(angle) = opposite/adjacent
tan(angle) = 130/170
angle ≈ 37.19 degrees
So, the angle between the diagonals of this rectangle is approximately 37.19 degrees. Just remember to tell the rectangle to keep its "acute" sense of humor!
To find the angle between the diagonals of a rectangle, we can use the formula:
angle = arctan(b/a)
Where a and b represent the lengths of the rectangle's sides.
In this case, a = 170mm and b = 130mm.
So, let's substitute the values into the formula:
angle = arctan(130/170)
Now, we can calculate this using a scientific calculator or an online calculator:
angle ≈ arctan(0.765) ≈ 37.21 degrees
Therefore, the angle between the diagonals of the rectangle is approximately 37.21 degrees.
To find the angle between the diagonals of a rectangle, we can use the trigonometric concept called "arctan" or "inverse tangent."
Let's consider the given rectangle with sides measuring 170mm and 130mm.
First, we need to find the length of the rectangle diagonals using the Pythagorean theorem. The diagonal of a rectangle can be found using the formula:
diagonal = √(length^2 + width^2)
For our rectangle, the length is 170mm and the width is 130mm. Plugging these values into the formula, we get:
diagonal = √(170^2 + 130^2)
= √(28900 + 16900)
= √(45800)
≈ 214.55mm
Now that we know the length of the diagonals, we can find the angle between them using the inverse tangent function (arctan) and the relation given by:
Angle = arctan(length/width)
In our case, the length of the rectangle is 170mm, and the width is 130mm. Plugging these values into the formula, we get:
Angle = arctan(170/130)
≈ arctan(1.31)
≈ 53.66 degrees
So, the angle between the diagonals of the rectangle with sides 170mm and 130mm is approximately 53.66 degrees.