WEBVTT
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Find the length π΄π΅, giving your answer to two decimal places.
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The length π΄πΆ in the diagram is 39 centimetres.
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And the angle π΅π΄πΆ is equal to 37 degrees.
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As the triangle is right-angled, we can solve this problem using the trigonometrical ratios.
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Sin π is equal to the opposite divided by the hypotenuse.
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Cos π is equal to the adjacent divided by the hypotenuse.
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And tan π is equal to the opposite divided by the adjacent.
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In this example, weβre looking to calculate the length π΄π΅, labelled π₯ on the diagram.
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The length π΄πΆ is the hypotenuse of the triangle as it is the longest side and itβs opposite the right angle.
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π΅πΆ is the opposite as it is opposite the 37-degree angle.
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And π΄π΅ is the adjacent as it is next to or adjacent to the 37- and 90-degree angles.
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As we are going to use the adjacent and the hypotenuse, weβll use the cosine ratio.
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Cos π equals the adjacent divided by the hypotenuse.
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Substituting in our values from the diagram gives us cos 37 is equal to π₯ divided by 39.
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Multiplying both sides of this equation by 39 gives us 39 multiplied by cos 37 is equal to π₯.
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This gives a value of π₯ of 31.15.
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This means that the length of π΄π΅ is 31.15 centimetres to two decimal places.