• # How to find the diagonal of the rectangle?

Alena Tikhonova
February 1, 2013
66073

The task of finding the diagonal of a rectangle can be formulated in three different ways. Let us consider in more detail each of them. The methods depend on the known data, so how to find the diagonal of the rectangle?

## If his two sides are known

In the case when two sides of the rectangle a and b are known, to find the diagonal, it is necessary to use the Pythagorean theorem: a2+ b2= c2, here a and b are the legs of a right triangle, c is the hypotenuse of a right triangle. When a diagonal is drawn in a rectangle, it is divided into two right triangles. The two sides of this right triangle are known to us (a and b). That is, to find the diagonal of a rectangle, the formula is needed as follows: c = √ (a2+ b2), here with - the length of the diagonal of the rectangle.

## On the known side and the corner, between the side and the diagonal

Let the side of the rectangle a and the angle it forms with the diagonal of the rectangle α be known. To begin with, we recall the cosine formula: cos α = a / c, here c is the diagonal of the rectangle.How to calculate the diagonal of a rectangle from this formula: с = a / cos α.

## On the known side, the angle between the adjacent side of the rectangle and the diagonal.

Since the diagonal of the rectangle divides the rectangle itself into two right triangles, it is logical to refer to the definition of sine. Sine - the ratio of the leg opposite this angle to the hypotenuse. Sin α = b / c. From here we derive a formula for finding the diagonal of a rectangle, which is also the hypotenuse of a right triangle: c = b / sin α.

Now you are savvy in this matter. You can please the geometry teacher tomorrow!

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