# How to prove that this triangle is right-angled?

##
Letters a, b and c are for the angles of a triangle.

How to prove that

if #cot(a/2) = (sinb + sinc)/(sin a)# , than is the triangle right-angled

Letters a, b and c are for the angles of a triangle.

How to prove that

if

##### 2 Answers

If you have all three side lengths, to be right angled the triangle must obey Pythagorus's theorem.

#### Explanation:

eg.

if triangle has side lengths of 3, 4 and 5;

Hence triangle is right angled.

If however, the triangle has side lengths of 3, 4 and 6;

and triangle is NOT right angled.

Hope it helps :)

Kindly refer to a **Proof** given in the **Explanation.**

#### Explanation:

Given

Also, we know that,

Now,

Taking into a/c that

**not possible,** or,

This proves that