Regarding the question in the image,I worked out that the area of the triangle OCD is $120 \text{ cm}^2$ (I used base X height x $1/2$). However, when I tried to work out the angle COD, I worked "backwards" using the formula $(1/2) \text { }ab \sin C$ and the answer I got for the size of angle COD was 0.98 radians (to 2 decimal places).
When I used a different method by splitting triangle OCD in half and using the sine ratio that the opposite side (here $15$ cm) divided by the hypotenuse (here $17$ cm) gives half of the sine of the angle required. Using this method, I got the answer $2.16$ radians (for the full angle COD).
The answer at the back of the book is $2.16$ (my second answer).
Please can someone tell me why my first method was wrong? Thanks
The problem is that the angle is obtuse. In the first answer, you have actually calculated $\pi-C$ instead of $C$. The second method is simpler, since you know you are dealing with an acute angle, since it is one of the angles of a right triangle. In the first method, further steps are required to determine whether the angle is acute or obtuse.