Math Problem Statement

determin the type of triangle

Determine the type of triangle that is drawn below.

Solution

Let's analyze the given triangle to determine its type.

Information provided:

  • Sides:
    NO=5.32NO = 5.32,
    OM=4.4OM = 4.4,
    NM=7.43NM = 7.43
  • Angles:
    N=36\angle N = 36^\circ,
    O=99\angle O = 99^\circ,
    M=45\angle M = 45^\circ

Steps:

  1. Check for right angles: There is no 9090^\circ angle, so it's not a right triangle.
  2. Check for side lengths:
    • The three sides are of different lengths (5.325.32, 4.44.4, and 7.437.43). This makes the triangle scalene (no two sides are equal).
  3. Check for the type of angles:
    • One angle is obtuse (O=99\angle O = 99^\circ), meaning the triangle has one angle greater than 9090^\circ, making it obtuse.

Conclusion:

This triangle is Scalene Obtuse, as it has all sides of different lengths and one obtuse angle.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

  1. What defines a scalene triangle?
  2. How do you determine whether a triangle is obtuse or acute?
  3. What are the properties of an isosceles triangle?
  4. Can a triangle have more than one obtuse angle?
  5. What role does the sum of angles play in classifying triangles?

Tip: Remember, the sum of all interior angles in a triangle always equals 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Classification
Angle Properties
Side Lengths

Formulas

Sum of angles in a triangle = 180°
Classification of triangles by angles and sides

Theorems

Triangle Angle Sum Theorem
Scalene Triangle Theorem

Suitable Grade Level

Grades 7-9