Question

Decide whether the conditions create a unique triangle, multiple triangles, or no triangle.

Given (triangle ABC).
(AB = 2.5) cm
(BC = 4) cm
(∠ B = 120^∘)

a. Unique Triangle
b. Multiple Triangles
c. No Triangle
d. None

Answer 1

The given conditions create a unique triangle.

Step-by-step explanation:

This question is asking whether the given conditions create a unique triangle, multiple triangles, or no triangle.

Here are the conditions:

• Side AB = 2.5 cm
• Side BC = 4 cm
• Angle B = 120 degrees

In order to determine if a triangle can be formed, we need to check if the sum of the lengths of any two sides is greater than the length of the third side, and if any two angles add up to less than 180 degrees. Let's check:

• AB + BC = 2.5 + 4 = 6.5 cm, which is greater than the third side AC
• Angle A + Angle B + Angle C = 180 degrees

Therefore, the given conditions create a unique triangle.