1. Tardigrade
  2. Question
  3. Mathematics
  4. Two medians drawn from acute angles vertices of a right angled triangle intersects at an angle (π /6) . If the length of the hypotenuse of the triangle is 3 units, then area of the triangle (in sq. units) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Two medians drawn from acute angles vertices of a right angled triangle intersects at an angle $\frac{\pi }{6}$ . If the length of the hypotenuse of the triangle is $3$ units, then area of the triangle (in sq. units) is

NTA AbhyasNTA Abhyas 2020

Solution:

Slope of $A G = - \frac{b}{2 a} , \, tan 30^{o} = \frac{\frac{3 b}{2 a}}{1 + \frac{b^{2}}{a^{2}}}$
Solution
$a^{2}+b^{2}=9\Rightarrow \frac{1}{\sqrt{3}}=\frac{3 b . a}{2 \left(a^{2} + b^{2}\right)}$
$\Rightarrow \, \frac{1}{2} \, ab=\left(\frac{a^{2} + b^{2}}{3 \sqrt{3}}\right)=\frac{9}{3 \sqrt{3}}=\sqrt{3}$