5th grade level Sasha says that she drew in acute isosceles triangle with silence of 6 cm 9 cm and 12 cm and angles of 30 50 and 100 Daniel says that is not possible explain using sides and angles who is correct

Answer 1

To determine who is correct, let's analyze the claims made by Sasha and Daniel regarding the triangle.

Sasha's Triangle:

• Sides: 6 cm, 9 cm, and 12 cm
• Angles: 30 degrees, 50 degrees, and 100 degrees

Angle Analysis:

1. For any triangle, the sum of all angles must equal 180 degrees. Let's add Sasha's angles:
   • 30 + 50 + 100 = 180 degrees
   • This is correct since it sums to 180 degrees.

Side Analysis:

2. A triangle can be classified based on its angles:

   • Acute triangle: All angles are less than 90 degrees.
   • Obtuse triangle: One angle is greater than 90 degrees.
   • Right triangle: One angle is exactly 90 degrees.

   In Sasha's case, one angle is 100 degrees, which is greater than 90 degrees. Thus, this triangle is not an acute triangle but an obtuse triangle.

3. Now let's check if a triangle can exist with the sides 6 cm, 9 cm, and 12 cm:

   • One way to check if three sides can form a triangle is to use the triangle inequality theorem, which says the sum of the lengths of any two sides must be greater than the length of the third side.
   • Check all three combinations:
     • 6 cm + 9 cm > 12 cm → 15 > 12 (True)
     • 6 cm + 12 cm > 9 cm → 18 > 9 (True)
     • 9 cm + 12 cm > 6 cm → 21 > 6 (True)

Since all the inequalities hold true, the sides do indeed form a triangle.

Conclusion:

• While the sides can form a triangle, the angles do not correspond to an acute triangle due to the presence of a 100-degree angle. Thus, Sasha’s assertion of an "acute isosceles triangle" is incorrect. Daniel is correct in stating that Sasha's claims about the triangle were not possible because you cannot have an acute triangle with an angle measuring 100 degrees.

So, Daniel is right. The triangle cannot be an acute triangle based on the angles Sasha provided.