Properties of Triangles 3 Question 4

4. Which of the following pieces of data does not uniquely determine an acute angled $\triangle A B C$ ( $R$ being the radius of the circumcircle)?

(2002, 1M)

(a) $a, \sin A, \sin B$

(b) $a, b, c$

(c) $a, \sin B, R$

(d) $a, \sin A, R$

Show Answer

Answer:

Correct Answer: 4. (d)

Solution:

  1. First solve each option separately.

(a) If $a, \sin A, \sin B$ are given, then we can determine $b=\frac{a}{\sin A} \sin B, c=\frac{a}{\sin A} \sin C$. So, all the three sides are unique.

So, option (a) is incorrect.

(b) The three sides can uniquely make an acute angled triangle. So, option (b) is incorrect.

(c) If $a, \sin B, R$ are given, then we can determine $b=2 R \sin B, \sin A=\frac{a \sin B}{b}$. So, $\sin C$ can be determined.

Hence, side $c$ can also be uniquely determined.

(d) If $a, \sin A, R$ are given, then

$$ \frac{b}{\sin B}=\frac{c}{\sin C}=2 R $$

But this could not determine the exact values of $b$ and $c$.



NCERT Chapter Video Solution

Dual Pane