Height on Longer Side of Scalene Triangle Given Medium Side and Smaller Angle Calculator

Formula Used:

\[ Height_{Longer} = S_{Medium} \times \sin(\angle_{Smaller}) \]

Height on Longer Side of Scalene Triangle:

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1. What is the Height on Longer Side of Scalene Triangle?

The Height on Longer Side of Scalene Triangle is the length of the perpendicular from the longer side of the Scalene Triangle to the opposite vertex. It is an important geometric measurement used in various calculations involving scalene triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Height_{Longer} = S_{Medium} \times \sin(\angle_{Smaller}) \]

Where:

\( S_{Medium} \) — Medium Side of Scalene Triangle (m)
\( \angle_{Smaller} \) — Smaller Angle of Scalene Triangle (degrees)
\( \sin \) — Sine trigonometric function

Explanation: The formula calculates the height on the longer side using the medium side length and the sine of the smaller angle in the triangle.

3. Importance of Height Calculation

Details: Calculating the height on the longer side is crucial for determining the area of the scalene triangle, solving geometric problems, and understanding the triangle's spatial properties.

4. Using the Calculator

Tips: Enter the medium side length in meters and the smaller angle in degrees. All values must be valid (side length > 0, angle between 0-180 degrees).

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 the sine function in this calculation?
A: The sine function relates the opposite side (height) to the hypotenuse (medium side) in a right triangle formed by the height perpendicular to the longer side.

Q3: Can this formula be used for any triangle?
A: This specific formula is designed for scalene triangles where you know the medium side and the smaller angle adjacent to the height being calculated.

Q4: What units should I use for the inputs?
A: The medium side should be in meters and the angle in degrees. The calculator will output the height in meters.

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 measurements.