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The height of an equilateral triangle is a perpendicular line drawn from any vertex to the opposite side. When given the exradius (radius of the escribed circle), the height can be calculated using a specific mathematical relationship.
The calculator uses the formula:
Where:
Explanation: This formula establishes a direct proportional relationship between the height of an equilateral triangle and its exradius, where the height equals the exradius value.
Details: Calculating the height of an equilateral triangle is essential in various geometric applications, construction projects, and engineering designs where precise measurements of triangular structures are required.
Tips: Enter the exradius value in meters. The value must be positive and valid for accurate calculation.
Q1: What is an exradius in an equilateral triangle?
A: The exradius is the radius of an escribed circle (excircle) of the triangle, which is a circle tangent to one side of the triangle and the extensions of the other two sides.
Q2: Why is the formula h = re/1 so simple?
A: In an equilateral triangle, there's a fixed mathematical relationship between various elements. The height equals the exradius in this specific case.
Q3: Can this formula be used for all types of triangles?
A: No, this specific formula applies only to equilateral triangles where all sides and angles are equal.
Q4: What are practical applications of this calculation?
A: This calculation is useful in architecture, engineering design, and any field requiring precise geometric measurements of equilateral triangular structures.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles, providing precise height measurements when given the correct exradius value.