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Not Between

Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 26 of 44.

Two sides and an angle look like SAS at first glance. Check where the angle sits. If it is not between the two sides, it faces one of them, the pair is complete, and the law of sines is the tool: the ambiguous case.

$Triangle ABC with A = 40°, BC = 8 and AC = 11$

A = 40°, a = BC = 8 and b = AC = 11. The 40° touches AC but not BC, so it faces BC: a pair. Then sin(beta) = 11sin(40°)/8, about 0.8839, and β is about 62.11° or 117.89°. Both leave room for 40°, so there are two triangles.

Challenge

In triangle ABC, the angle at A is 38°, BC = 9 cm and AC = 14 cm. Find every possible angle θ at B, to two decimal places. Choose the law yourself, then press Check.

Try it yourself

$Use the figure to find theta$

Use the figure to find theta

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Triangles Without Right Angles

1Across the Lake

Across the Lake Sines Past 90°Cosines Past 90°Recap: Across the River

4Law of Cosines: SAS

The Law of Cosines An Obtuse Angle Between Through the Hill A Hooked Drive Recap: Two Sides, One Angle

7Area of a Triangle

Area With a Sine Area With an Obtuse Angle Working Backwards The Angle From the Area Heron's Formula Recap: A Garden Bed

2Law of Sines: AAS and ASA

Why the Law of Sines Holds Pair Side With Angle The Third Angle First Two Coast Stations Recap: Law of Sines

5Law of Cosines: SSS

Three Sides, One Angle The Largest Angle A Triangular Field Recap: Three Sides

8Bearings and Navigation

Reading Bearings Two Ships From Port Turning Off Course Finding a Course Angle Recap: Ships at Sea

3The Ambiguous Case

Finding an Angle Two Triangles The Height Test An Obtuse Given Angle Radio Coverage Recap: How Many Triangles?

6Which Law to Use

Sines or Cosines?Not BetweenThree Towns Recap: Pick the Law

9Final Challenges

Final: Across the Canyon Final: Every Triangle Final: A Plot of Land Final: Ship and Plane Final: The Largest Angle