18. In the figure, ABC is a triangular piece of paper such that ZABC=45, ZACB=30 and...

 

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18. In the figure, ABC is a triangular piece of paper such that ZABC=45, ZACB=30 and AC=2. D is the foot of perpendicular from A to BC. (a) Find AB, BD and DC. (b) 30 A 2 2 D C E D 45% B B (3 marks) The paper is folded along AD. It is then placed on a horizontal table such that the edges AB and AC lie on the table and the plane DAB is vertical. E is the foot of perpendicular from D to AB. (i) If is the angle between DC and the horizontal, show that sin0 = 6 6 (ii) Find CE. Hence show that ZEAC=45. (iii) Find the angle between the two planes DAB and DAC to the nearest degree. (8 marks) 18. In the figure, ABC is a triangular piece of paper such that ZABC=45, ZACB=30 and AC=2. D is the foot of perpendicular from A to BC. (a) Find AB, BD and DC. (b) 30 A 2 2 D C E D 45% B B (3 marks) The paper is folded along AD. It is then placed on a horizontal table such that the edges AB and AC lie on the table and the plane DAB is vertical. E is the foot of perpendicular from D to AB. (i) If is the angle between DC and the horizontal, show that sin0 = 6 6 (ii) Find CE. Hence show that ZEAC=45. (iii) Find the angle between the two planes DAB and DAC to the nearest degree. (8 marks)