Find-all-triangles-with-consecutive-integer-sides-and-having-an-angle-twice-another-angle-

Question Number 516 by 112358 last updated on 25/Jan/15

F i n d a l l t r i a n g l e s w i t h c o n s e c u t i v e

i n t e g e r s i d e s a n d h a v i n g a n a n g l e t w i c e

a n o t h e r a n g l e .

Commented by prakash jain last updated on 22/Jan/15

a = n

b = n + 1

c = n + 2

\cos A = \frac{(n + 5)}{2 (n + 2)}

\cos B = \frac{n^{2} + 2 n + 3}{2 n (n + 2)}

\cos C = \frac{(n - 3)}{2 n}

B = 2 A, C = 2 B, C = 2 A

All equation give no integer solution

except n = 1, which does not form

a triangle .

So the given question does not have a

solution .