Oblique Triangle Angle Calculation

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Oblique Triangle Angle Calculation

Oblique Triangle Angle Calculation
\[A=\sin^{-1}\left(\frac{a\sin(B)}{b}\right)\]

Variables

A = unknown triangle angle (rad or °)
a = side opposite angle A (m)
b = side opposite angle B (m)
B = known triangle angle (rad or °)

Description

What is this formula?


This trigonometric formula calculates an unknown angle in an oblique triangle using the Law of Sines.


An oblique triangle is any triangle that does not contain a right angle. The Law of Sines relates the sides of a triangle to the sines of their opposite angles.


This method allows the determination of an unknown angle when two sides and one opposite angle are known.


When to use it


Use this formula when:


- The triangle is not a right triangle

- Two side lengths are known

- One opposite angle is known

- An unknown angle must be calculated

- Solving geometry, surveying, or navigation problems


This formula is commonly used for SSA triangle configurations.


Example


If:


a = 8 m

b = 12 m

B = 50°


Then:


A = asin((8*sin(50°))/12)


A ≈ 30.71°


Applications


- Trigonometry and geometry

- Civil engineering

- Surveying and mapping

- Navigation calculations

- Physics and mechanics

- Educational mathematics

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