In the diagram, ADC is a straight line and BFC is a straight line. CDEF is a rectangle. EF = 4cm and ED = 5 cm. <DAE = 20 degrees and <EBF = 30 degrees. Calculate the length in cm of 1. BF. 2. AB

a)
1. Find the length DF using Pythagoras' theorem.
2. Then, deduce the length of CE.
3. Using the tangent ratio, find the length of BC.
4. BC = 5 + BF. Since you now know BC, you can find BF.

b) For this one, I hope you know the cosine and sine rules... I can't find a simpler way to do it.
1. Find the angle ACE using any 2 of the three sides of the triangle CDE and using the appropriate trigonometric ratio.
2. Hence find the angle AEC.
3. Using the sine rule, find the length of AC (using angle ACE, and CAE, sides AC and CE).
4. Using the cosine rule again, find the length of AB (using angle ACB, and sides BC and AC).

Hello sir... thanks a lot for the brilliant answer... I appreciate it highly