Sine rule ambiguous case

A complete lesson on the scenario of using the sine rule to find an obtuse angle in a triangle. Given the connection this has with triangle congruence and the graph of sine, these ideas are also explored in the lesson. Designed to come after pupils have spent time doing basic sine rule questions and have also encountered the graph of sine beyond 90 degrees.

Activities included:

Starter:
A goal-free question to get pupils thinking, that should help recap the sine rule and set the scene for the rest of the lesson.

Main:

• A prompt for pupils to construct a triangle given SSA, then a closer look at both possible answers. Depending on the class, this could be a good chance to talk about SSA being an insufficient condition for congruence.
• A related question on finding an unknown angle using the sine rule. Pupils know there are two answers (having seen the construction), but can they work out both answers?
• This leads into a closer look at the symmetry property of the sine graph, and some quick questions on this theme for pupils to try.
• Then back to the previous question, to find the second answer. This is followed by four similar questions for pupils to practice (finding an obtuse angle using the sine rule)
• Two extension questions.

Plenary:
A slide to summarise the lesson as simply as possible.

Answers and printable worksheets included.

Please review if you buy as any feedback is appreciated!