To be used only with side-side-non-included angle triangles.
For all other triangles, click here.

The diagram above shows 3 instances of triangles with 2 known sides and one known
non-included angle. The known angle is shown in all 3 possible positions.
(Known information is in red, calculated information is in black).

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Side Side Angle Calculator

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This diagram shows the different triangles which can result
when 2 sides are known, the known angle (A) is less than 90° and is not the included angle.

The length of side a will determine how many solutions you will get.
The height of triangle ABC (line BC) = side a • sine (angle A) and so if:
• side a (blue line) < BC (height) - no solution because side a doesn't "reach" point C.
• side a (blue line plus red line) = BC (height) - one solution. Side a just "reaches" line BC and forms a right angle at point C.
• side a (the orange lines) > BC (height) but < side c - two solutions. This is the ambiguous case. Side a has gone beyond point C and now can intersect the triangle at points c_{1} and c_{2}.
• side a (black line BD) >= side c - one solution. Side a is now so long that it can only intersect the triangle at point D. Unlike the ambiguous case, there can't be a matching "left side" for line BD because it is so long, it can no longer intersect the triangle.

This diagram is similar to the previous one except the known angle (A) can be from 90°
to 180°.
Again, the length of side a determines the solutions.
• side a is less than or equal to side c - no solution. Side a is "contained" within side c.
• side a is greater than side c - one solution.
There is no ambiguous case because side b has no "left side" where side a can intersect.

For practice with the calculator, imagine you have a 30-60-90 triangle whose
sides are 1, 1.73205 and 2.
Although this diagram shows right triangles, this calculator works with all types of
triangles.)
It is important that side C be the side between the known angle and the
known side.