trigonometry part 2

Pythagoras’s Theorem

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
i.e.: c² = a² + b² in the following diagram:

image: http://revisionworld.com/sites/revisionworld.com/files/imce/trig3.gif

A right angled triangleExample

Find AC in the diagram below.

AB² + AC² = BC²
AC² = BC² – AB²
= 13² – 5²
= 169 – 25 = 144
AC  = 12cm

image: http://revisionworld.com/sites/revisionworld.com/files/imce/Pythag.gif

Pythagoras Theorem

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Pythagoras’s Theorem

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
i.e.: c² = a² + b² in the following diagram:

image: http://revisionworld.com/sites/revisionworld.com/files/imce/trig3.gif

A right angled triangleExample

Find AC in the diagram below.

AB² + AC² = BC²
AC² = BC² – AB²
= 13² – 5²
= 169 – 25 = 144
AC  = 12cm

image: http://revisionworld.com/sites/revisionworld.com/files/imce/Pythag.gif

Pythagoras Theorem

This video explains how to work out phytagoras theorem

3D Problems (Higher Tiers)

In higher tier papers, you may be asked to solve 3d problems using Pythagoras.

Example

A cuboid has sides of length 10cm, 2 √11 cm and 5cm. Find the length of a diagonal.

image: http://revisionworld.com/sites/revisionworld.com/files/imce/py3d1.GIF

A cuboidSo we want to find AD.

We can draw a right-angled triangle inside the cuboid which has AD as it’s hypotenuse. Then we can use Pythagoras.

image: http://revisionworld.com/sites/revisionworld.com/files/imce/py3d2.GIF

A  right-angled triangle with AD as it's hypotenuseTo use Pythagoras, we need to know AC and CD. We know that CD is 5 cm. We need to find AC.

We can use Pythagoras to find AC, because if we look at the cuboid from above, we see that AC is the diagonal of a rectangle

image: http://revisionworld.com/sites/revisionworld.com/files/imce/py3d3.GIF

AC is the  diagonal of a rectangleABC is a right angled triangle, so by Pythagoras, AC2 = AB2 + BC2
= 102 + (2 √11)2 = 100 + 44 = 144

Now we can find AD: AD2 = AC2 + CD2 = 144 + 25 = 169
Therefore AD = 13

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