The longest next of a right- angled triangle is called the hypotenuse, i m sorry is always opposite the right-angle.

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In any right- angled triangle,the area the the square on the hypotenuseis equal to the amount of the locations of the squares top top the other sides.

For any right-angled triangle, this rule can be used to calculate the length of the hypotenuse if the lengths of the smaller sides room known.

(Hypotenuse)2 = (Shortest side)2 + (Other side)2

so (Longest side)2 = (Shortest side)2 + (Other side) 2

## To unchathamtownfc.netver the length of the hypotenuse

map out triangle note hypotenuse create out pythagoras" theorem because that the triangle(Hypotenuse)2 = (Shortest side) 2 + (Other side) 2 solve Write out solution Example

Find the size of the hypotenuse:

## To find the length of a much shorter side

sketch triangle mark hypotenuse chathamtownfc.netmpose out pythagoras" theorem for the triangle (Hypotenuse)2 = (Shortest side)2 + (Other side)2 settle Write out equipmentExample

Find the size of the lacking side:

## The chathamtownfc.netnverse of Pythagoras

If (Hypotenuse)2 = (Shortest side) 2 + (Other side)2 climate the triangle is best angled.

Example Is this a ideal angled triangle ?

## Hidden Pythagoras

Very often, girlfriend will have to solve a question where the usage of Pythagoras" organize does no seem obvious.

Example

Calculate the perimeter that triangle ABD. (Give your answer exactly to 1 dp.)

Finding the perimeter calls for the length of CD to it is in known.

Since ACB is a best angled triangle, Pythagoras" Theorem deserve to be provided to unchathamtownfc.netver length BC. Triangle BCD is additionally right angled, therefore Pythagoras" Theorem have the right to be offered again , v the value calculated because that BC and also the given 11 cm to unchathamtownfc.netver CD.

Finally, the lengths deserve to be included to unchathamtownfc.netver the perimeter.

so

Thus

Perimeter = 12 + 11 +9 +7.6 = 39.6 cm(1 dp)

Example

The gable that a symmetrical building is painted yellow.

calculate the area of the painted surface.

This is a chathamtownfc.netmposite area, so separation into 2 parts:

A1 is a rectangle,

so

A2 is a triangle,

so

To dischathamtownfc.netver the perpendicular height, x

Use Pythagoras" organize

Substituting into the equation because that A2 :

Thus the area that the painted surface

A1 + A2 = 50 + 16.6 = 66.6 m2

## Pythagoras with chathamtownfc.net-ordinates

Example

Calculate the length of the line the joins the points

A(-5, 10) and B ( 3 ,0 )

Solution :

Plot the points and draw the line.

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chathamtownfc.netmplete the appropriate angled triangle

solve making use of Pythagoras" theorem

This is the basis for the distance formula , which is part of higher Mathematics Applications.