trig question...what am i doing wrong?

There is a probability that the answer sheet is WRONG... Too bad it tries to trick you then...

...BUT the info "DB=18.4cm" really pricks my mind. Was it calculated from previous part of the question and rounded off to 1 d.p.?

If so, I've checked it out (haha~). If DB is actually 18.43 or 18.44 cm angle BAD will be 66.4`````````

Look at your given. It says AD = 20 cm and DA = 10 cm. I believe one of these is the real AD and the other one is AB.

Now, assuming AD = 20 cm and AB = 10 cm, then
Using the Cosine Law, we have
angle BAD = arccos({BD^2 - [(AD^2) + (AB^2)]}/[-2(AD)(AB)])
angle BAD = arccos({18.4^2 - (20^2) - (10^2)]}/[-2(20)(10)])
angle BAD = 66.2

You're right.

Hope this helps.

teddy boy

You have given the measurements of sides incorrectly

AD and DA are the same sides

But using 18.4cms as the side opposite the required angle
and the Cosine Rule I also get 66.19 degrees which is 66.2 to 2 decimal places

You wrote AD= 20cm, but DA=10cm..... or do you mean BA=10cm?

If BA=10cm;

Then you'd use the cosine formula giving BAD as 66.197= 66.2

I think either you misread the question or the marking scheme is wrong; since your answer is correct given the above information.

I get 66.2 too. Maybe the answer sheet is wrong.