Which of the following sets of data does not | vedclass

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

Question

(D) In $\Delta ABC$,the Sine Rule states $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R$.For option $(a)$: Given $a, \sin A, \sin B$. Fr

Vedclass · Accepted Answer

$a, \sin A, R$

Vedclass · Answer

(D) In $\Delta ABC$,the Sine Rule states $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R$.For option $(a)$: Given $a, \sin A, \sin B$. From $\frac{a}{\sin A} = 2R$,we find $R$. Then $b = 2R \sin B$ and $c = 2R \sin C = 2R \sin(180^{\circ} - (A+B)) = 2R \sin(A+B)$. Thus,the triangle is uniquely determined.For option $(b)$: Given $a, b, c$. By the $SSS$ congruence criterion,the triangle is uniquely determined.For option $(c)$: Given $a, \sin B, R$. We have $b = 2R \sin B$. Now we have two sides $a, b$ and the circum-radius $R$. Since $\sin A = \frac{a}{2R}$,angle $A$ is determined. Thus,the triangle is uniquely determined.For option $(d)$: Given $a, \sin A, R$. We have $\frac{a}{\sin A} = 2R$. This is an identity that holds for any triangle with side $a$ and angle $A$ having circum-radius $R$. It does not provide enough information to fix the other sides or angles. Therefore,the triangle is not uniquely determined.

Which of the following sets of data does not uniquely determine an acute-angled $\Delta ABC$ ($R$ = circum-radius)?

Similar Questions

In $\triangle ABC$,if $a=3, b=4, c=6$,then $\frac{\cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}}{\cot A+\cot B+\cot C}=$

The area of an isosceles triangle is $9 \, cm^2$. If the equal sides are $6 \, cm$ in length,the angle between them is .... $^\circ$.

If the angles of a triangle $ABC$ are in the ratio $1: 2: 3$,then the corresponding sides are in the ratio

In $\Delta ABC,$ if ${a^2} + {b^2} + {c^2} = ac + ab\sqrt{3},$ then the triangle is:

In a $\triangle ABC$,the sides $a, b, c$ are in $A$.$P$. if and only if $r_1, r_2, r_3$ are in

Vedclass Test Series

Exam Paper Generator

Online Exam Module