In-a-triangle-the-length-of-the-two-larger-sides-are-24-and-22-respectively-If-the-angles-are-in-AP-then-the-third-side-is-

Question Number 41079 by nadeem last updated on 01/Aug/18

In a triangle the length of the two

larger sides are 24 and 22, respectively .

If the angles are in AP, then the third

side is

Answered by tanmay.chaudhury50@gmail.com last updated on 01/Aug/18

l e t a n g l e s a r e A - \propto, A, A + \propto

A - \propto + A + A + \propto= 180^{o}

3 A = 180^{o} A = 60^{o}

u n k n o e n s i d e b e x

c o s A = \frac{x^{2} + 24^{2} - 22^{2}}{2 x . 24}

\frac{1}{2} = \frac{x^{2} + 46 \times 2}{2 . x . 24}

24 x = x^{2} + 92

x^{2} - 24 x + 92 = 0

x = \frac{24 - \sqrt{576 - 368}}{2} = \frac{24 - 14.42}{2} = \frac{9.58}{2} = 4.79

w e c a n n o t t a k e \frac{24 + \sqrt{576 - 368}}{2} s i n c e

24 i s g r e a t e s t s i d e a s p e r q u e s t i o n

c o s (A - \propto) = \frac{24^{2} + 22^{2} - 4 . 79^{2}}{2.24.22}

A - \propto= {c o s}^{- 1} (\frac{24^{2} + 22^{2} - 4 . 79^{2}}{2.24.22})

A + . \propto= {c o s}^{- 1} (\frac{22^{2} + 4 . 79^{2} - 24^{2}}{2.22.4.79})