Question

The cosine of the obtuse angle formed by the medians from the vertices of the acute angles of an isosceles right angled triangle is

• A. $-2/3$
• B. $-4/5$
• C. $-3/5$
• D. $-3/4$

Answer 1

The correct option is B $-4/5$

we have to find

$\cos \theta$ (In figure)

$m_{c_E}=\frac{-\frac{a}{2}}{a}=\frac{-1}{2}$

$m_{A_D}=\frac{-a}{\frac{a}{2}}=-2$

$\therefore \tan (\pi -\theta )=\mid \frac{(-2)+\frac{1}{2}}{1+1}\mid$

$\tan (\pi -\theta )=\frac{3}{4}$

$-\tan \theta =\frac{3}{4}$

$\cos (\pi -\theta )=\frac{4}{5}$

$\begin{array}{cc}-\cos \theta & =\frac{4}{5}\\ \cos \theta & =\frac{-4}{5}\\ \text{option B is correct}& \end{array}$