Math Problem Statement
Which angle in triangle DEF has the largest measure? Given that side DF = 6, side EF = 7, and side DE = 11.
Solution
To determine which angle in triangle has the largest measure, we can use the property of triangles that states:
In a triangle, the largest angle is opposite the longest side.
From the diagram:
- Side has a length of 6,
- Side has a length of 7,
- Side has a length of 11.
Since is the longest side, the angle opposite this side is .
Therefore, is the largest angle in triangle .
The correct answer is C. .
Would you like further clarification or have any questions?
Here are 5 related questions:
- How can the Law of Cosines be used to find specific angles in a triangle?
- What are the other properties of a triangle related to angle and side measures?
- How do the angles of a triangle sum up, and how is this fact used in problems?
- Can we determine specific angle measures without using side lengths?
- What is the relationship between an equilateral triangle’s sides and angles?
Tip: In any triangle, the angle opposite the longest side will always be the largest.
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangle Properties
Formulas
In a triangle, the largest angle is opposite the longest side.
Theorems
Triangle Inequality Theorem
Properties of Triangles
Suitable Grade Level
Grades 6-8