Oblique Triangle Angle Calculation

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

Variables

Aunknown triangle angle (rad or °)

aside opposite angle A (m)

bside opposite angle B (m)

Bknown 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