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# Kinda Pythagorean Theorem

Let be a triangle such that , and . Find the area of the triangle.

Solution

Since it follows from the law of sines that

Hence . Thus,

To completely justify the title of the post we give another solution based on the following proposition:

Proposition: Let be a given triangle such that . Prove that

Proof: We are working on the following figure.

Let be the bisector of . Then:

and the result follows.

Now, the area of the initial triangle is given by Heron’s formula.