Hi,
For this Q https://imgur.com/a/ffr3c
How is the answer getting tantheta = 1/2?
This is the very last Q of VCAA 2011 E1 if you need more context.
Thanks
From part c, we know that BD and CD are in the ratio 1:2. The triangle is also right-angled. The ratio itself is sufficient to be able to use the pythagorean theorem.
If you're still not sure how this can be true, consider that since the ratio of BD:CD is always 1:2, then their lengths can be written as k and 2k respectively, where k is any positive real number. The hypotenuse side will also remain in ratio with these two sides.
So, using pythagoras' theorem
^2+(2k)^2=(ck)^2 \text{ where c is a constant})

Divide both sides by k
2
and we can get our result as desired.
Hope this helps
