## Mathematics Support Materials

### Mathematics snapshot: Pythagoras’ Theorem

Mathematics/Measurement and Geometry/Pythagoras and trigonometry

Content Description Relevant aspects of the Achievement Standards

Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (ACMMG222)

Apply trigonometry to solve right-angled triangle problems (ACMMG224)

Students use Pythagoras’ Theorem and trigonometry to find unknown sides of right-angled triangles

### Nature of the assessment

Anecdotal evidence based on teacher observation

### Purposes of the assessment

To assess the students’ ability to identify and use an appropriate model to determine unknown lengths and angles in right triangles.

### Stage in the teaching sequence

Towards the end of a lesson sequence

The students were required to solve each of the following problems.

1. A pergola is to be built with a gabled roof as shown. What is the length of AB, the slant height of the gable?

2. A footing underneath a 65 m tall building has become unstable and, as a result, the building currently leans at an angle of 4 to the vertical (as shown below). Determine the vertical distance. ### Assessment process

Working in pairs, the students had to decide whether each problem could be solved using Pythagoras’ Theorem or trigonometry, based on the key information in each scenario. The students were then required to apply the appropriate model and determine the length of the unknown side in question. 