Question

If one angle of a triangle is ${30}^o$ and the lengths of the sides adjacent to it are $40$ and $40\sqrt{3}$, the triangle is?

• A. right angled
• B. isosceles
• C. obtuse angled
• D. none of these

Answer 1

Answer: (B), (C)

The correct options are
B isosceles
C obtuse angled

Let the unknown side be $x$.
Hence
$cos{30}^0=\frac{{40}^2+(40\sqrt{3}{)}^2-x^2}{2\left(160\sqrt{3}\right)}$
$\frac{\sqrt{3}}{2}=\frac{{40}^2+(40\sqrt{3}{)}^2-x^2}{2\left(1600\sqrt{3}\right)}$
$4800={40}^2+(40\sqrt{3}{)}^2-x^2$
$({40}^2-x^2)=0$
$x=40$
Hence two sides are equal.
Hence the triangle is an isosceles triangle.