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

Formula Used:

\[ \text{Smaller Angle of Scalene Triangle} = \arcsin\left(\frac{\text{Shorter Side of Scalene Triangle}}{\text{Medium Side of Scalene Triangle}} \times \sin(\text{Medium Angle of Scalene Triangle})\right) \]

Shorter Side of Scalene Triangle:

Medium Side of Scalene Triangle:

Medium Angle of Scalene Triangle:

rad

Smaller Angle of Scalene Triangle:

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1. What is the Smaller Angle of Scalene Triangle?

The Smaller Angle of Scalene Triangle is the measure of the wideness of sides that join to form the corner opposite the shorter side of the Scalene Triangle. In a scalene triangle, all three sides and angles are different, making this calculation essential for understanding the triangle's geometry.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Smaller Angle} = \arcsin\left(\frac{\text{Shorter Side}}{\text{Medium Side}} \times \sin(\text{Medium Angle})\right) \]

Where:

Shorter Side — Length of the shorter side of the triangle (m)
Medium Side — Length of the medium side of the triangle (m)
Medium Angle — Angle opposite to the medium side (rad)

Explanation: This formula uses the sine rule and inverse sine function to calculate the smaller angle based on the given side lengths and medium angle.

3. Importance of Smaller Angle Calculation

Details: Calculating the smaller angle is crucial for complete geometric analysis of scalene triangles, determining triangle properties, and solving various trigonometric problems in mathematics and engineering applications.

4. Using the Calculator

Tips: Enter the shorter side and medium side in meters, and the medium angle in radians. All values must be positive numbers greater than zero.

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: The trigonometric functions in the formula work with radians. If you have degrees, convert them to radians first (radians = degrees × π/180).

Q3: What if the calculated angle is not valid?
A: The formula ensures the result is a valid angle between 0 and π/2 radians (0-90 degrees) for the smaller angle of a triangle.

Q4: Can this formula be used for other triangle types?
A: While derived for scalene triangles, this formula can be applied to any triangle where you know the required side lengths and angles.

Q5: What are the limitations of this calculation?
A: The calculation assumes valid triangle properties (sum of angles = π radians, triangle inequality theorem holds).