Question

Which of the following measures would create two possible triangles?

three angles: 26°, 48°, and 106°
three sides: 5 cm, 9 cm, and 15 cm
an angle of 48° found between two sides: 4 cm and 6 cm
two sides, 4 cm and 6 cm, with an angle of 48° not found between them

Below in bold.
Step-by-step explanation:
The three angles of a triangle add up to 180 degrees.
106 + 26 + 48 = 180
So this will give a triangle.
In a triangle, the sum of any 2 of the sides must be greater that the other side.
So,  in the case of sides 5,  9 and 15 cm ,  5 + 9 < 15 so these
will not give a triangle.
An angle of 48 between sides 4 and 6 cm:
Using the Cosine Rule to find the other side x:
x^2 = 4^2 + 6^2 – 2.4.6cos48
x^2 = 18.88 so x = 4.46 cm
So the 3 sides are 4 , 4.5 and 6 cm long
this will make a triangle
An angle not betweem side  of 4 and side of 6/
applying sine rule:
4 /sin 48 = 6 / sin x
sin x = 5 sin 48 / 4 = 1.1147
As yhe sine of an angle must b between – 1 and 1 no angle is possible so no trangle can be draw.