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**by P Rowell Tile Hill Wood School**

Trigonometry by P Rowell Tile Hill Wood School

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**Triangles -the basics In any triangle the three angles add up to 180°**

One of the angles in a right angle triangle is 90° The hypotenuse is the side opposite the right angle and is always the longest side of a right angle triangle

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Pythagoras In any right angle triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. h2 = a2 + b2 h a b

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**Naming the sides hypotenuse hypotenuse opposite adjacent adjacent**

The hypotenuse is always the side opposite the right angle. The opposite and adjacent sides are dependent on where the angle is

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Trigonometry

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Trigonometry

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Trigonometry

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Trigonometry

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Trigonometry

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**Trigonometry – The Sine Ratio**

For a given angle the ratio of the opposite side and the hypotenuse is always the same. We call this ratio the Sine Ratio The sine ratio links three things the size of an angle , the length of the side opposite the angle and the length of the hypotenuse. If we are given the values for two of these we can find the value of the third

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Example Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long 12m h 40°

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Example Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long Hyp 12m h Opp 40° Adj Step 1: Label the sides

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Example Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long Hyp 12m h Opp 40° Adj Step 1: Label the sides Step 2: Cross out the side you don’t need

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Example Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long Hyp 12m h Opp 40° Adj Step 1: Label the sides Step 2: Cross out the side you don’t need Step 3: Decide which ratio you need to use O SOH CAH TOA S X H

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Example Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long Hyp 12m h Opp 40° Adj Step 1: Label the sides Step 2: Cross out the side you don’t need Step 3: Decide which ratio you need to use Step 4: Cover up what you want to find O S X H

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Example Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long Hyp 12m h Opp 40° Step 4: Cover up what you want to find Step 5: Write down the calculation S X H

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Ratios for Right Angle Triangles. Sine = opposite hypotenuse Cosine = opposite hypotenuse Tangent = opposite adjacent Sin = OCos = ATan = O H H.

Ratios for Right Angle Triangles. Sine = opposite hypotenuse Cosine = opposite hypotenuse Tangent = opposite adjacent Sin = OCos = ATan = O H H.

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