In a triangle ABC, if a sin A = b sin B, then | vedclass

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

Question

(C) Using the Sine Rule,we know that $\frac{a}{\sin A} = \frac{b}{\sin B} = 2R,$ where $R$ is the circumradius of the triangle.This implies $\sin A =

Vedclass · Accepted Answer

$a = b$

Vedclass · Answer

(C) Using the Sine Rule,we know that $\frac{a}{\sin A} = \frac{b}{\sin B} = 2R,$ where $R$ is the circumradius of the triangle.This implies $\sin A = \frac{a}{2R}$ and $\sin B = \frac{b}{2R}.$Substituting these into the given equation $a \sin A = b \sin B$:$a \left( \frac{a}{2R} \right) = b \left( \frac{b}{2R} \right)$$\frac{a^2}{2R} = \frac{b^2}{2R}$$a^2 = b^2$Since $a$ and $b$ are side lengths of a triangle,they must be positive,so $a = b.$Thus,the triangle is isosceles.

In a triangle $ABC,$ if $a \sin A = b \sin B,$ then the nature of the triangle is:

Similar Questions

In $\Delta ABC,$ if $\cot A, \cot B, \cot C$ are in $A.P.,$ then $a^2, b^2, c^2$ are in

In a $\triangle ABC$,if $\angle C = 90^{\circ}$,then $\frac{a^2-b^2}{a^2+b^2}$ is equal to

In $\triangle ABC$,if $(a-b)(s-c)=(b-c)(s-a)$,then $r_1, r_2, r_3$ are in

If $A, B, C$ are the angles of a triangle with $\tan \frac{A}{2}=\frac{1}{3}$ and $\tan \frac{B}{2}=\frac{2}{3}$,then the value of $\tan \frac{C}{2}$ is:

If in a $\triangle ABC$,$\frac{1}{a+c} + \frac{1}{b+c} = \frac{3}{a+b+c}$,then $\angle C$ is equal to (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module