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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. h 2 = a 2 + b 2 h a b

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Naming the sides hypotenuse adjacent opposite hypotenuse adjacent opposite 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 – 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 40° 12m Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long h

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

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Example 40° 12m Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long h Step 1: Label the sides Step 2: Cross out the side you dont need Hyp Opp Adj

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Example 40° 12m Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long h Step 1: Label the sides Step 2: Cross out the side you dont need Step 3: Decide which ratio you need to use Hyp Opp Adj O S X H SOH CAH TOA

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Example 40° 12m Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long h Step 1: Label the sides Step 2: Cross out the side you dont need Step 3: Decide which ratio you need to use Step 4: Cover up what you want to find Hyp Opp Adj O S X H

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

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