When you have a right triangle there are 5 things you can know about it..:

When you have a right triangle there are 5 things you can know about it.. the lengths of the sides (A, B, and C) the measures of the acute angles (a and b) (The third angle is always 90 degrees) A C B a b

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If you know two of the sides, you can use the Pythagorean theorem to find the other side But what happens if you wan to know the angles? Or if you have angles and you want to find the sides?

Some terminology::

Some terminology: Before we can use trigonometry we need to get a few terms straight The hypotenuse ( hyp ) is the longest side of the triangle – it never changes The opposite ( opp ) is the side directly across from the angle you are considering The adjacent ( adj ) is the side right beside the angle you are considering

A picture always helps…:

A picture always helps… looking at the triangle in terms of angle b A C B b adj hyp opp b C is always the hypotenuse A is the adjacent (near the angle) B is the opposite (across from the angle) Longest Near Across

But if we switch angles…:

But if we switch angles… looking at the triangle in terms of angle a A C B a opp hyp adj a C is always the hypotenuse A is the opposite (across from the angle) B is the adjacent (near the angle) Longest Across Near

Lets try an example:

Lets try an example Suppose we want to find angle a what is side A? the opposite what is side B? the adjacent A = 3 C B = 4 a b

ACTIVITY:

ACTIVITY Draw a triangle What do we notice? Opposite Adjacent Hypotenuse O/H A/H O/A Complete the table (round your answers to 2dp)

The Ratios:

The Ratios Yes, so there are three sets of ratios for any triangle They are mysteriously named: sin …short for sine cos …short for cosine tan …short or tangent and the ratios are already calculated, you just need to use them

So what are the formulas?:

So what are the formulas? SOH CAH TOA You can use this word if you need to memorize the formulas!

Remember the Mnemonic SOH CAH TOA:

Remember the Mnemonic SOH CAH TOA Sense Of Humour Can Always Help To Overcome Awkwardness Silly Old Harry Thought Of A Cow And Horse Your turn to make a sentence

Finding Lengths….:

Finding Lengths….

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Example One

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Example two

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Example Three

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Example Four

Finding Angles:

Finding Angles

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Example One

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Example two

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Example Three

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