Question

lf one angle of a triangle is ${30}^0$ and the lengths of the sides adjacent to it are $40$ and $40$ $\sqrt{3}$, then the triangle is

• A. equilateral
• B. right angled
• C. isosceles
• D. scalene

Answer 1

Answer: (C)

isosceles

$\cos {30}^0=\frac{{\left(40\right)}^2+{\left(40\sqrt{3}\right)}^2-d^2}{2\times 40\times 40\sqrt{3}}$......(using cos formula $\cos A=\frac{b^2+c^2-a^2}{2bc}$)

$\frac{\sqrt{3}}{2}\times 2\times 40\times 40\sqrt{3}={\left(40\right)}^2+{\left(40\sqrt{3}\right)}^2-d^2$

$d^2=1600$
$d=40$
$\therefore$ Triangle is isosceles.