Hard question on Similar Triangle and Trigonometry

The name of the textbook is:
New Zealand Mathematics second edition 10

Published by Haese & Harris Publications Ltd (Auckland New Zealand)

This is a second edition published long time ago back in 2002, so the current one might be better with corrections, but I am not sure...

The thing is that the proofreaders did not do their job properly!

(By the way, here in New Zealand, most of textbooks are so terrible with full of errors. Quite a long time ago, when I was working on a Year 9 New Zealand mathematics textbook, I found about 50 errors even if I had not finished 2/3 of the book! So I rang up the publisher to complain about it, but they have no manner whatsoever so they did not even apologize for so many errors in the book. They also told me that they would make corrections. However, even though that was about a decade ago, and there are still many errors in the books with no correction whatsoever. The customer service in New Zealand is so notorious and bad enough for me to escape from this country for good next month.)
Dennis must be ancient if 2002 was a long time ago!
 
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