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If a=10 inches and b=24 inches, a) What would c have to be to make it an acute triangle? b) What would c have to be to make it a right triangle? c) What would c have to be to make it an obtuse triangle?

User Tizz
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1 Answer

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Final answer:

The type of triangle can be determined by side lengths. For an acute triangle, 'c' should be less than 26 inches. For a right triangle, 'c' should be ~26 inches. For an obtuse triangle, 'c' should be more than 26 inches.

Step-by-step explanation:

The type of triangle in your question can be determined by the lengths of the sides. Given your sides a=10 inches and b=24 inches, the length of the side c will determine the type of triangle.

a) For an acute triangle, c should be less than the square root of (a² + b²), which is less than √676 or less than 26 inches

b) For a right triangle, c should be equal to the square root of (a² + b²), which equals ~26 inches

c) For an obtuse triangle, c should be greater than the square root of (a² + b²), which is more than 26 inches

This is derived from the Pythagorean theorem: a² + b² = c², where c is the hypotenuse of a right triangle.

A triangle is a polygon with three edges and three vertices. It is one of the simplest and most fundamental shapes in geometry. The three sides of a triangle are segments that connect the three vertices, and the three angles of a triangle are the angles formed by these sides.

Key Concepts:

Vertices: The corners or points where the sides of the triangle meet are called vertices.

Edges or Sides: The line segments connecting the vertices are the sides or edges of the triangle.

Angles: The angles of a triangle are formed by the intersection of its sides. The sum of all interior angles in a triangle is always 180 degrees.

Learn more about Triangle Types

User Sylordis
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