Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2005  OctNov  (P19709/01)  Q#3
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Question
In the diagram, ABED is a trapezium with right angles at E and D, and CED is a straight line.
The lengths of AB and BC are and respectively, and angles BAD and CBE are and respectively.
i. Find the length of CD in terms of .
ii. Show that angle CAD =
Solution
From the given information we can compile following data;
i.
It is evident from the diagram that;
We can find from ;
Expression for trigonometric ratio in righttriangle is;
From the given diagram for ;
We can find from ;
Expression for trigonometric ratio in righttriangle is;
From the given diagram for ;
It is evident from the diagram that;
Hence;
Now we can substitute the values in equation;
ii.
Expression for trigonometric ratio in righttriangle is;
It is evident from the diagram that for ;
From (i) we know that;
To find , it is evident from the diagram that;
It is also evident from the diagram that;
Therefore;
Now we find out .
Expression for trigonometric ratio in righttriangle is;
For 
For 
From 
From 














Now we can substitute the values in the equation;
Finally we have the values to substitute in equation;
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