Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Law of Sines

Calculate the angles in a generic triangle.

The "Law of Sines" can be used to calculate the angles of a triangle.

Law of cosines

The "Law of Sines" can be expressed as

$$  {a  \over sin A } = {b  \over sin B } = {c  \over sin C }   \tag{1}$$

where

a, b and c = length of sides in triangle (m, ft ...)

A, B and C = angles in the triangle (degrees)

Law of Sines Calculator

Eq. 1 can be modified to

$$  a = {b sin A \over sin B }  =  {c sin A \over sin C } \tag{1a}$$

$$  b = {a sin B \over sin A }  =  {c sin B \over sin C } \tag{1b}$$

$$  c = {a sin C \over sin A }  =  {b sin C \over sin B } \tag{1c}$$

This expression can also be handy:

$$  sin \frac{1}{2}A = \sqrt{{(s - b)(s - c) \over b c }}     \tag{2}$$

where

$$  s = \frac{1}{2}(a + b  + c)     \tag{3}$$

Related Topics

  • Mathematics

    Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

Related Documents

Search

Search is the most efficient way to navigate the Engineering ToolBox.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about

We use a third-party to provide monetization technologies for our site. You can review their privacy and cookie policy here.

You can change your privacy settings by clicking the following button: .

Citation

This page can be cited as

  • The Engineering ToolBox (2013). Law of Sines. [online] Available at: https://www.engineeringtoolbox.com/law-of-sines-d_1858.html [Accessed Day Month Year].

Modify the access date according your visit.

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter

















































5.3.10

.