Question

A right-angled playing ground is to be constructed with other interior angles as ${30}^o$ and ${60}^o.$ Is this information sufficient for the construction concerning the outline of the playground?

• A. No, only two dimenisons are provided which is insufficient to determine the shape and size of the area.
• B. Yes, only three dimenisons are required to determine the shape and size of the area.
• C. No, the area can be of any size with the given information.

Answer 1

The correct option is C No, the area can be of any size with the given information.

The interior angles are ${30}^o,{60}^o$ and ${90}^o.$
Hence AAA information is provided.

With only the three angles, the shape of the ground can be determined, but the size is not fixed.

Consider the following example:


The triangle $△PQR$ has a hypotenuse of 50 m, and $△XYZ$ has a hypotenuse of 30 m.

Hence, there are many possibilities regarding the size of the ground.