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# Sine rule - ambiguous case visualiser
- URL: https://www.esheets.io/sine-rule-ambiguous-case-visualiser/
- Published: 2026-07-05T14:12:46.000Z
- Updated: 2026-07-05T14:36:09.000Z
- Author: Richard Linnington 2
- Tags: Maths, Tools, Geometry and Shape

The **sine rule ambiguous case** happens when the information you are given can produce more than one possible triangle. This can occur when you know two sides and an angle that is not between them.

Use the interactive visualiser below to change the angle and side lengths. Watch how the circle intersects the ray from A and see when **no triangle, one triangle or two different triangles** are possible.

The visualiser also links the geometry to the sine rule calculation, helping to explain why a second possible angle can appear.

Interactive maths visualisation

## Explore the sine rule ambiguous case

Change the known angle and side lengths. The dashed circle shows every possible position of B that keeps **BC = a**. Watch what happens where the circle meets the ray from A.

Angle A 

35°

Side a 

7.0 cm

Side b 

10.0 cm

Jump to: No triangle Just touches Two triangles One triangle 

Sine rule ambiguous case diagram A ray from A and a circle centred at C. Circle intersections show possible positions for B. 

Possible triangle All points a cm from C 

Current geometry

### Two triangles are possible

The circle cuts the ray twice, so there are two valid positions for B.

### What does the sine rule give?

sin B / b = sin A / a

sin B = 0.819

B = sin⁻¹(0.819) = 55.0°

Second possible angle: 180° − 55.0° = 125.0°

Show both First solution Second solution 

### Where is the ambiguous range?

Here, h = b sin A = 5.74 cm. Two triangles are possible when 5.74 < a < 10.00.

No triangle Two triangles One triangle 

h = **5.74** b = **10.00** 

At **a = h**, the circle just touches the ray, so there is exactly one right-angled triangle.

Finished? Why not try our [sine rule ambiguous case worksheet](https://www.esheets.io/sine-rule-ambiguous-case/)?