The ratio of the sides of triangle ABC is 1:s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given the ratio of sides $a:b:c = 1:\sqrt{3}:2$.Let $a = \lambda$,$b = \sqrt{3}\lambda$,and $c = 2\lambda$.Using the Law of Cosines,$\cos A = \fra

Vedclass · Accepted Answer

$1:2:3$

Vedclass · Answer

(D) Given the ratio of sides $a:b:c = 1:\sqrt{3}:2$.Let $a = \lambda$,$b = \sqrt{3}\lambda$,and $c = 2\lambda$.Using the Law of Cosines,$\cos A = \frac{b^2 + c^2 - a^2}{2bc} = \frac{3\lambda^2 + 4\lambda^2 - \lambda^2}{2(\sqrt{3}\lambda)(2\lambda)} = \frac{6\lambda^2}{4\sqrt{3}\lambda^2} = \frac{\sqrt{3}}{2}$.Thus,$A = 30^\circ$.Similarly,$\cos B = \frac{a^2 + c^2 - b^2}{2ac} = \frac{\lambda^2 + 4\lambda^2 - 3\lambda^2}{2(\lambda)(2\lambda)} = \frac{2\lambda^2}{4\lambda^2} = \frac{1}{2}$.Thus,$B = 60^\circ$.Finally,$C = 180^\circ - (30^\circ + 60^\circ) = 90^\circ$.The ratio $A:B:C = 30^\circ:60^\circ:90^\circ = 1:2:3$.

The ratio of the sides of triangle $ABC$ is $1:\sqrt{3}:2$. The ratio of angles $A:B:C$ is

Similar Questions

The two adjacent sides of a cyclic quadrilateral are $2$ and $5$ and the angle between them is $60^o$. If the third side is $3$,the remaining fourth side is

In a $\triangle ABC$,$A = 30^{\circ} + C$ and $R = (\sqrt{3} + 1)r$,where $r$ is the inradius and $R$ is the circumradius. Then:

In $\triangle ABC$,if $a=5$ and $\tan \frac{A-B}{2}=\frac{1}{4} \tan \frac{A+B}{2}$,then $\sqrt{a^2-b^2}=$

If the sides of a triangle are $p, q$ and $\sqrt{p^2 + pq + q^2}$,then the largest angle is

In triangle $ABC$,if $a=13, b=8, c=7$,then $\cos(B+C) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module