Problem—uva -10522

Problem—UVA -10522

 


Now given 3 sides Ha, Hb and Hc. We have to calculate the area A.

If three sides are a, b and c we can have -

Now from 1 and 2, we can get

From (4) and (5)

As Ha, Hb and Hc given, we got the ratio of a, b and c.

So there will be a k, for which

If the angles are A, B and C. We know that -

So,

Now, from sin rule

From (7) and (9)  we get

We know Ha, Hb, Hc, and k, so we can calculate the exact value of a, b and c. So we can calculate the area of triangle by the following formula -

This was my solution.

While discussing my solution with Nafi, he gave me a much smarter solution, Here it is
Area

So

Similarly,

Now,

And,