The sides of a triangle are(x + 4)cm, xcm and (x - 4)cm, respectively If the cosine of the largest angle is \(\frac{1}{5}\), find the value of x
A. 24cm B. 20cm C. 28cm D. 7cm E. \(\frac{88}{7}\)
Correct Answer: A
Explanation
< B is the largest since the side facing it is the largest, i.e. (x + 4)cm Cosine B = \(\frac{1}{5}\) = 0.2 given b2 - a2 + c2 - 2a Cos B Cos B = \(\frac{a^2 + c^2 - b^2}{2ac}\) \(\frac{1}{5}\) = \(\frac{x^2 + ?(x - 4)^2 - (x + 4)^2}{2x (x - 4)}\) \(\frac{1}{5}\)= \(\frac{x(x - 16)}{2x(x - 4)}\) \(\frac{1}{5}\) = \(\frac{x - 16}{2x - 8}\) = 5(x - 16) = 2x - 8 3x = 72 x = \(\frac{72}{3}\) = 24
