Shorter Side of Scalene Triangle given Smaller Angle, Medium Angle and Medium Side Calculator

Formula Used:

\[ S_{Shorter} = S_{Medium} \times \frac{\sin(\angle_{Smaller})}{\sin(\angle_{Medium})} \]

Medium Side of Scalene Triangle:

Meter

Smaller Angle of Scalene Triangle:

Radian

Medium Angle of Scalene Triangle:

Radian

Shorter Side of Scalene Triangle:

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1. What is the Shorter Side of Scalene Triangle?

The Shorter Side of Scalene Triangle is the length of the shortest side out of the three sides. In a scalene triangle, all sides have different lengths, and the shorter side is opposite the smallest angle of the triangle.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

\[ S_{Shorter} = S_{Medium} \times \frac{\sin(\angle_{Smaller})}{\sin(\angle_{Medium})} \]

Where:

\( S_{Shorter} \) — Shorter Side of Scalene Triangle (Meter)
\( S_{Medium} \) — Medium Side of Scalene Triangle (Meter)
\( \angle_{Smaller} \) — Smaller Angle of Scalene Triangle (Radian)
\( \angle_{Medium} \) — Medium Angle of Scalene Triangle (Radian)

Explanation: This formula uses the Law of Sines to calculate the shorter side when the medium side and two angles are known.

3. Importance of Triangle Side Calculation

Details: Calculating triangle sides is fundamental in geometry, engineering, architecture, and various technical fields where precise measurements and spatial relationships are crucial.

4. Using the Calculator

Tips: Enter the medium side length in meters, and both angles in radians. All values must be positive numbers within valid ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is a scalene triangle?
A: A scalene triangle is a triangle with all three sides of different lengths and all three angles of different measures.

Q2: Why use radians instead of degrees?
A: Trigonometric functions in mathematical calculations typically use radians. If you have angles in degrees, convert them to radians first (radians = degrees × π/180).

Q3: Can this formula be used for any triangle?
A: This specific formula applies to scalene triangles where you know the medium side and the angles opposite the shorter and medium sides.

Q4: What if I know different combinations of sides and angles?
A: Other formulas from the Law of Sines can be used depending on which sides and angles are known.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. The accuracy depends on the precision of your input measurements.