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

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## Description

5.1 Surface Area
5.2 Similarity
5.3 Trigonometry
5.4 Non-Right Angled Triangles
5.5 Spherical Geometry

Outcome Key knowledge • angle properties of triangles, Pythagoras' theorem, the trigonometric ratios sine, cosine and tangent, methods for solving non-right-angled triangles (including the ambiguous case of the sine rule) and their application • the rules for calculating the surface area and volume of spheres, cylinders, cones, pyramids and prisms, and their composites • three figure bearings and their application • the rule $\displaystyle s=r \times \frac{\pi}{180} \times \theta^{\circ}$ for determining the length of an arc of a circle • a sphere of radius 6400 km as a model of the earth, great circles (meridians) and small circles (parallels), latitude and longitude (specified in decimal degrees).Key skills • solve practical problems involving the calculation of the side lengths, angles and areas of triangles, including the construction of diagrams based on word descriptions • solve practical problems involving the calculation of the surface area and volume of spheres, cylinders, prisms and their composites • solve practical problems involving the use of a linear scale factor to scale lengths, areas and volumes of similar figures and shapes • use a sphere of radius 6400 km as a model of the earth to solve practical problems involving meridians and parallels and latitude and longitude (specified in decimal degrees) • use the concept of a great circle to find the shortest distance between two points on the earth’s surface with the same longitude • solve time zone problems.