FUNDING AREA OF A TRIANGLE WHEN TWO ANGLES AND THE SIDE BETWEEN THEN ARE GIVEN

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Previously, I showed you how to find area of a triangle when two sides and the angle between them are given CHECK HERE.Today I am gonna show you how to find the same when two angles and the side between them are given as you seen in cover photo.Now check the figure below and try to find out area of the triangle.

To solve this we need a formula and which is given by
∆= sinB×sinC×a.Simply putting the values of sinB , sinC and side a we can easily find the area.Before heading to the solution , I wanna show how can the formulla be derived. To construct the formulla , we need to know a few related formullae also.I proved the formullae in my previous posts. When I use a formulla , the link of it's derivation article will also be given below the figures. If you find problem to understand those formullae ,you can check them first.

First we have to know sine rule.Check it in the
figure below: CHECK SINE RULE HERE

Then we need to know area of a triangle when two sides and angle between are given. Check it in the figure below: CHECK AREA OF ∆ HERE

Once we understand sine rule and formula of area of a triangle when two sides and the angle between are given, we can conclude another formula which has been proved in the figure below:

Now from sine rule and formulla of area of a triangle [∆=abc/4R] , we can conclude the required formulla which we need to solve today's problem.Check the proof in the figure below:

I hope you already know the area.As we got the required formulla proved , now it's time for the solution.Check the easiest solution in the figure below:

The article is made keeping in mind all kinds of reader and for that I have to get every detailing I needed to prove the required formulla to solve the problem.

All the drawing and figure used in the article are made by me using cell phone applications namely math editor and a good text editor.Mistake can be happen while I was constructing it ; If there any mistake ,please ignore it or let me know. I tried my best make it look perfect. I may overlook something. Excuse me for that.😀

I hope you find this article informative and interesting.

Thank you so much for visiting.

Have a good day.

All is well.

Regards: @meta007