cmi-entrance 2021 Q3

cmi-entrance · India · ugmath 4 marks Sine and Cosine Rules Ambiguous case and triangle existence/uniqueness
We want to construct a triangle ABC such that angle A is $20.21 ^ { \circ }$, side AB has length 1 and side BC has length $x$ where $x$ is a positive real number. Let $N ( x ) =$ the number of pairwise noncongruent triangles with the required properties.
(a) There exists a value of $x$ such that $N ( x ) = 0$.
(b) There exists a value of $x$ such that $N ( x ) = 1$.
(c) There exists a value of $x$ such that $N ( x ) = 2$.
(d) There exists a value of $x$ such that $N ( x ) = 3$.
We want to construct a triangle ABC such that angle A is $20.21 ^ { \circ }$, side AB has length 1 and side BC has length $x$ where $x$ is a positive real number. Let $N ( x ) =$ the number of pairwise noncongruent triangles with the required properties.

(a) There exists a value of $x$ such that $N ( x ) = 0$.\\
(b) There exists a value of $x$ such that $N ( x ) = 1$.\\
(c) There exists a value of $x$ such that $N ( x ) = 2$.\\
(d) There exists a value of $x$ such that $N ( x ) = 3$.