# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | 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 right-triangle is; From the given diagram for ;       We can find from ; Expression for trigonometric ratio in right-triangle 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 right-triangle 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 right-triangle is; For For From From               Now we can substitute the values in the equation;   Finally we have the values to substitute in equation;     