Question

Which of the following measures would create two possible triangles?

Answer Choices:
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

Answer 1

The answer is three angles: 26°, 48°, and 106°

because the interior angles of a triangle must always add up to 180°:
26 + 48 + 106 = 180 ✅

Answer 2

Below in bold.

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.