Question

A triangular-shaped park is to be constructed in a middle of a city with dimensions of approximately 1 kilometer, 1.6 kilometers and 40°. Will any triangle with the given dimensions be identical in shape and size? Answer in Yes/No.

Answer 1

The given dimensions are 1 kilometer, 1.6 kilometers and 40°.
Hence, these are two sides and one angle.

If the dimensions are in the order Side-Angle-Side, then any triangular shape will be congruent and identical in shape and size.

However, if these dimensions are in the order Side-Side-Angle, then the triangles will not be congruent.

Consider the following figure:


Here, the side with 1 km can touch the base at $R$ or $R^{\prime },$ which will result in two different shapes.

Hence, any triangle with the given dimensions will not be identical in shape and size.