Oblique Triangle Side Calculation

\[a = \frac{b\sin(A)}{\sin(B)}\]

Variables

aunknown triangle side (m)

bknown triangle side (m)

Aangle opposite side a (rad or °)

Bangle opposite side b (rad or °)

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

An oblique triangle is any triangle that does not contain a 90° angle. The Law of Sines relates side lengths to the sines of their opposite angles.

This method allows the determination of unknown sides when one side and two angles are known.

Use this formula when:

- The triangle is not a right triangle

- One side length is known

- Two angles are known

- An unknown side must be calculated

- Solving geometry, surveying, or navigation problems

This formula is especially useful for ASA and AAS triangle configurations.

If:

b = 12 m

A = 40°

B = 65°

Then:

a = (12*sin(40°))/sin(65°)

a ≈ 8.51 m

- Trigonometry and geometry

- Civil engineering

- Surveying and mapping

- Navigation calculations

- Physics and mechanics

- Educational mathematics