Question

The three sides a, b, c and three angles A, B, C are called elements of triangle ABC. We can evaluate all the six elements uniquely if any three of them are given.

• A. True
• B. False

Answer 1

The correct option is B False

Let's start by dividing the possibilities one by one.
Case i: 3 sides are given.
Here we can compute all the angles using trigonometric Ratios of half angles. (There are other methods too).
Case ii: a, b and Included angle C.
Using Napier's analogy and A + B + C = ${180}^{\circ }$, we can compute angles and the side c as well.
Case iii: a, b and angle A.
Here using sine rule we can compute angle B then C then side c.
The case where 2 angles and 1 side are given can be solved using sine rule as all angles are known $(A+B+C={180}^{\circ })$
Case iv: A, B, C are given
In this case $\infty$ triangles are possible as all the triangles with the given angles are similar.
Therefore the elements cannot be evaluated uniquely.
Therefore given statement is false in general.