# VCE Further Mathematics Units 3 and 4 – Geometry and Measurement

5.1 Surface Area

5.2 Similarity

5.3 Trigonometry

5.4 Non-Right Angled Triangles

5.5 Spherical Geometry

This module covers the use of measurement, geometry and trigonometry to formulate and solve problems involving angle, length, area and volume in two and three dimensions, with respect to objects, the plane and the surface of the earth.

Measurement and trigonometry, including:

- calculation of surface area and volume of spheres, cylinders, cones, pyramids and prisms, and their composites
- application of linear scale factor \( k > 0 \) of similar figures and shapes to scale lengths, areas and volumes with practical applications
- review of the methods for solving right and non-right-angled triangles, including the ambiguous case of the sine rule, and their application to solving practical problems in two and three dimensions
- specification of location (distance and direction) in two dimensions using three-figure bearings with applications such as navigation and orienteering, including situations involving the solution of non-right-angled triangles.

Spherical geometry, including:

- circle mensuration; arc length using the rule \( \displaystyle s = r \times \frac{\pi}{180} \times \theta^{\circ} \) with practical applications
- arc length of a sector of a circle, and the areas of sectors and segments with practical applications
- use of trigonometry and Pythagoras’ theorem in two and three dimensions to solve problems involving the solution of right-angled triangles within a sphere
- use of a sphere of radius 6400 km as a model of the earth, and meridians and parallels and their use in locating points on the surface of the earth in terms of latitude and longitude (specified in decimal degrees) using the Greenwich meridian and the equator as reference
- use of meridians to determine the shortest distance from any point on the earth to a pole or the equator
- use of a great circle to determine the shortest distance between two points on the surface of the earth that have the same longitude
- use of 15° of longitude as equating to a 1 hour time difference to identify time zones, and determine travel times of journeys that cross two or more time zones from departure and arrival times.

*source – VCE Mathematics Study Design*

VCE Further Mathematics Units 3 and 4 Courses

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### Surface Area

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Similarity

Scale Factor
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Similar Triangles
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Scale Drawings
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Trigonometry

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True Bearings
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Obtuse Angles
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Non-Right Angled Triangles

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Spherical Geometry

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Time Zones
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