# How to calculate the sides of a triangle when only the area and 2 angles are given?

I'm reading the book 'Trig without tears' by Stan Brown and there is a table mentioning the method for finding the sides of a triangle (not only right triangles) when only the area and 2 angles are given. It wrote

'Find the third angle. Area = ½a b sin C, half of base × height, so substitute b = a×sin B/sin A from the Law of Sines (equation 28) and solve for a = √[2 Area × sin A / sin B sin C]. Then use the Law of Sines twice more to find the other two sides.'

I really can't understand it. Can anyone help me please?? Thanks!!!! :)

• We can't help you if we don't know why you can't follow it. That answer makes perfect sense and is straight forward. Where do you stop following. Finding the third angle? Knowing what area of a triangle is? Referring to the lengths by variables. The law of sines? Where? Jul 18 '16 at 5:54
• I can't understand this 'a = √[2 Area × sin A / sin B sin C].' why is it like this?? Jul 18 '16 at 6:41

$$b = a * {\sin B \over \sin A}$$
So, $$Area = 1/2 * a^2 * {\sin B * \sin C \over \sin A}$$