Question

A triangle is supposed to have the following characteristics: two sides have length 2 cms, and one of the angles is of size 60° . Does this information result in one triangle, two triangles, more than two triangles, or no triangle at all?
one triangle
two triangles
more than two triangles
no triangle at all

Answer 1

It results in one triangle.

Answer 2

can you explain why?

Answer 3

Lets try to form different triangles with the given data. The first is an isosceles triangle with two sides 2 cm and one included angle 60 degrees shown in the diagram below. In this case, since it is isosceles hence the other two angles will be equal so they need to be 60 and 60 each. Hence we now have an equilateral triangle with each side 2 cm.


The second triangle can have two sides 2 cm each while the angle 60 degrees can be an angle that is not included between the two sides. This is shown in the diagram below. However, since the two sides are equal so their corresponding base angles will be equal as well. So the other angle is also 60 degree here. As a result, the included angle has to be 60 again. So we again get an equilateral triangle with each side 2 cm.